Math / Algebra

QuestionSolve the equation: $m^{2}=18 m-80$ Answer: $m=$ $\square$ Write your answers as a list of integers or reduced fractions, with your answers separated by (a) comma(s). For example, if you get 4 and $-\frac{2}{3}$ as your answers, then enter $4,-2 / 3$ in the box.

Studdy Solution

STEP 1

What is this asking? Find the values of $m$ that make $m^2$ equal to $18m - 80$ . Watch out! Don't forget there might be more than one answer!

STEP 2

1. Rewrite the equation
2. Factor the quadratic
3. Solve for m

STEP 3

Let's rewrite our equation $m^2 = 18m - 80$ so that everything is on one side.
We want a zero on the other side because that lets us use a super cool trick later!

STEP 4

Subtract $18m$ from both sides: $m^2 - 18m = 18m - 80 - 18m$ .
This simplifies to $m^2 - 18m = -80$ .

STEP 5

Now, add 80 to both sides: $m^2 - 18m + 80 = -80 + 80$ .
This gives us $m^2 - 18m + 80 = 0$ .
Awesome!

STEP 6

Now, we factor this quadratic equation.
We're looking for two numbers that add up to $-18$ and multiply to $80$ .
Think, think, think!

STEP 7

How about $-8$ and $-10$ ?
Let's check! $-8 + (-10)$ is $-18$ , and $(-8) \cdot (-10)$ is $80$ .
Perfect!

STEP 8

So, we can rewrite our equation as $(m - 8)(m - 10) = 0$ .
This is the magic of factoring!

STEP 9

Now, we solve for $m$ .
If $(m - 8)(m - 10) = 0$ , then either $(m - 8) = 0$ or $(m - 10) = 0$ .
This is because anything multiplied by zero is zero!

STEP 10

If $m - 8 = 0$ , then we add 8 to both sides: $m - 8 + 8 = 0 + 8$ , so $m = 8$ .

STEP 11

If $m - 10 = 0$ , then we add 10 to both sides: $m - 10 + 10 = 0 + 10$ , so $m = 10$ .

STEP 12

So, our solutions are $m = 8$ and $m = 10$ .
We write this as $8, 10$ .

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QuestionSolve the equation: $m^{2}=18 m-80$ Answer: $m=$ $\square$ Write your answers as a list of integers or reduced fractions, with your answers separated by (a) comma(s). For example, if you get 4 and $-\frac{2}{3}$ as your answers, then enter $4,-2 / 3$ in the box.

Studdy Solution

STEP 1

What is this asking? Find the values of $m$ that make $m^2$ equal to $18m - 80$ . Watch out! Don't forget there might be more than one answer!

STEP 2

1. Rewrite the equation
2. Factor the quadratic
3. Solve for m

STEP 3

Let's rewrite our equation $m^2 = 18m - 80$ so that everything is on one side.
We want a zero on the other side because that lets us use a super cool trick later!

STEP 4

Subtract $18m$ from both sides: $m^2 - 18m = 18m - 80 - 18m$ .
This simplifies to $m^2 - 18m = -80$ .

STEP 5

Now, add 80 to both sides: $m^2 - 18m + 80 = -80 + 80$ .
This gives us $m^2 - 18m + 80 = 0$ .
Awesome!

STEP 6

Now, we factor this quadratic equation.
We're looking for two numbers that add up to $-18$ and multiply to $80$ .
Think, think, think!

STEP 7

How about $-8$ and $-10$ ?
Let's check! $-8 + (-10)$ is $-18$ , and $(-8) \cdot (-10)$ is $80$ .
Perfect!

STEP 8

So, we can rewrite our equation as $(m - 8)(m - 10) = 0$ .
This is the magic of factoring!

STEP 9

Now, we solve for $m$ .
If $(m - 8)(m - 10) = 0$ , then either $(m - 8) = 0$ or $(m - 10) = 0$ .
This is because anything multiplied by zero is zero!

STEP 10

If $m - 8 = 0$ , then we add 8 to both sides: $m - 8 + 8 = 0 + 8$ , so $m = 8$ .

STEP 11

If $m - 10 = 0$ , then we add 10 to both sides: $m - 10 + 10 = 0 + 10$ , so $m = 10$ .

STEP 12

So, our solutions are $m = 8$ and $m = 10$ .
We write this as $8, 10$ .

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Studdy Solution

STEP 1

What is this asking? Find the values of mmm that make m2m^2m2 equal to 18m−8018m - 8018m−80. Watch out! Don't forget there might be more than one answer!

STEP 2

1. Rewrite the equation2. Factor the quadratic3. Solve for *m*

STEP 3

Let's **rewrite** our equation m2=18m−80m^2 = 18m - 80m2=18m−80 so that everything is on one side.We want a zero on the other side because that lets us use a super cool trick later!

STEP 4

Subtract 18m18m18m from both sides: m2−18m=18m−80−18mm^2 - 18m = 18m - 80 - 18mm2−18m=18m−80−18m.This simplifies to m2−18m=−80m^2 - 18m = -80m2−18m=−80.

STEP 5

Now, add 80 to both sides: m2−18m+80=−80+80m^2 - 18m + 80 = -80 + 80m2−18m+80=−80+80.This gives us m2−18m+80=0m^2 - 18m + 80 = 0m2−18m+80=0.Awesome!

STEP 6

Now, we **factor** this quadratic equation.We're looking for two numbers that add up to −18-18−18 and multiply to 808080.Think, think, think!

STEP 7

How about −8-8−8 and −10-10−10?Let's check! −8+(−10)-8 + (-10)−8+(−10) is −18-18−18, and (−8)⋅(−10)(-8) \cdot (-10)(−8)⋅(−10) is 808080.Perfect!

STEP 8

So, we can rewrite our equation as (m−8)(m−10)=0(m - 8)(m - 10) = 0(m−8)(m−10)=0.This is the magic of factoring!

STEP 9

Now, we **solve** for mmm.If (m−8)(m−10)=0(m - 8)(m - 10) = 0(m−8)(m−10)=0, then either (m−8)=0(m - 8) = 0(m−8)=0 or (m−10)=0(m - 10) = 0(m−10)=0.This is because anything multiplied by zero is zero!

STEP 10

If m−8=0m - 8 = 0m−8=0, then we add 8 to both sides: m−8+8=0+8m - 8 + 8 = 0 + 8m−8+8=0+8, so m=8m = 8m=8.

STEP 11

If m−10=0m - 10 = 0m−10=0, then we add 10 to both sides: m−10+10=0+10m - 10 + 10 = 0 + 10m−10+10=0+10, so m=10m = 10m=10.

STEP 12

So, our **solutions** are m=8m = 8m=8 and m=10m = 10m=10.We write this as 8,108, 108,10.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? Find the values of $m$ that make $m^2$ equal to $18m - 80$ . Watch out! Don't forget there might be more than one answer!

1. Rewrite the equation
2. Factor the quadratic
3. Solve for m

Let's rewrite our equation $m^2 = 18m - 80$ so that everything is on one side.
We want a zero on the other side because that lets us use a super cool trick later!

Subtract $18m$ from both sides: $m^2 - 18m = 18m - 80 - 18m$ .
This simplifies to $m^2 - 18m = -80$ .

Now, add 80 to both sides: $m^2 - 18m + 80 = -80 + 80$ .
This gives us $m^2 - 18m + 80 = 0$ .
Awesome!

Now, we factor this quadratic equation.
We're looking for two numbers that add up to $-18$ and multiply to $80$ .
Think, think, think!

How about $-8$ and $-10$ ?
Let's check! $-8 + (-10)$ is $-18$ , and $(-8) \cdot (-10)$ is $80$ .
Perfect!

So, we can rewrite our equation as $(m - 8)(m - 10) = 0$ .
This is the magic of factoring!

Now, we solve for $m$ .
If $(m - 8)(m - 10) = 0$ , then either $(m - 8) = 0$ or $(m - 10) = 0$ .
This is because anything multiplied by zero is zero!

If $m - 8 = 0$ , then we add 8 to both sides: $m - 8 + 8 = 0 + 8$ , so $m = 8$ .

If $m - 10 = 0$ , then we add 10 to both sides: $m - 10 + 10 = 0 + 10$ , so $m = 10$ .

So, our solutions are $m = 8$ and $m = 10$ .
We write this as $8, 10$ .