QuestionSolve $8 x^{2}+56 x=0$ and identify the correct solutions: A. $x=7$ , B. $x=8$ , C. $x=0$ , D. $x=-7$ .

Studdy Solution

STEP 1

Assumptions1. We are given the quadratic equation $8x^{} +56x =0$ . We are looking for the solutions to this equation, i.e., the values of $x$ that make the equation true.

STEP 2

The first step in solving a quadratic equation is to set the equation to zero. In this case, the equation is already set to zero.
$8x^{2} +56x =0$

STEP 3

Next, we can simplify the equation by factoring out the greatest common factor from the left side of the equation. $x(8x +56) =0$

STEP 4

We can further simplify the equation by factoring out8 from the term in the parentheses.
$x(8(x +7)) =0$

STEP 5

Now we have a product of two terms equal to zero. According to the zero product property, if a product of factors is zero, then at least one of the factors must be zero.
So, we can set each factor equal to zero and solve for $x$ .
$x =0$ $8(x +7) =0$

STEP 6

olving the second equation for $x$ gives us $x + =0$

STEP 7

Subtract7 from both sides to isolate $x$ .
$x = -7$ So, the solutions to the equation $x^{2} +56x =0$ are $x =0$ and $x = -7$ .
Therefore, options C and D are correct.

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QuestionSolve $8 x^{2}+56 x=0$ and identify the correct solutions: A. $x=7$ , B. $x=8$ , C. $x=0$ , D. $x=-7$ .

Studdy Solution

STEP 1

Assumptions1. We are given the quadratic equation $8x^{} +56x =0$ . We are looking for the solutions to this equation, i.e., the values of $x$ that make the equation true.

STEP 2

The first step in solving a quadratic equation is to set the equation to zero. In this case, the equation is already set to zero.
$8x^{2} +56x =0$

STEP 3

Next, we can simplify the equation by factoring out the greatest common factor from the left side of the equation. $x(8x +56) =0$

STEP 4

We can further simplify the equation by factoring out8 from the term in the parentheses.
$x(8(x +7)) =0$

STEP 5

Now we have a product of two terms equal to zero. According to the zero product property, if a product of factors is zero, then at least one of the factors must be zero.
So, we can set each factor equal to zero and solve for $x$ .
$x =0$ $8(x +7) =0$

STEP 6

olving the second equation for $x$ gives us $x + =0$

STEP 7

Subtract7 from both sides to isolate $x$ .
$x = -7$ So, the solutions to the equation $x^{2} +56x =0$ are $x =0$ and $x = -7$ .
Therefore, options C and D are correct.

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QuestionSolve 8x2+56x=08 x^{2}+56 x=08x2+56x=0 and identify the correct solutions: A. x=7x=7x=7, B. x=8x=8x=8, C. x=0x=0x=0, D. x=−7x=-7x=−7.

Studdy Solution

STEP 1

Assumptions1. We are given the quadratic equation 8x+56x=08x^{} +56x =08x+56x=0 . We are looking for the solutions to this equation, i.e., the values of xxx that make the equation true.

STEP 2

The first step in solving a quadratic equation is to set the equation to zero. In this case, the equation is already set to zero.8x2+56x=08x^{2} +56x =08x2+56x=0

STEP 3

Next, we can simplify the equation by factoring out the greatest common factor from the left side of the equation.x(8x+56)=0x(8x +56) =0x(8x+56)=0

STEP 4

We can further simplify the equation by factoring out8 from the term in the parentheses.x(8(x+7))=0x(8(x +7)) =0x(8(x+7))=0

STEP 5

Now we have a product of two terms equal to zero. According to the zero product property, if a product of factors is zero, then at least one of the factors must be zero.So, we can set each factor equal to zero and solve for xxx.x=0x =0x=08(x+7)=08(x +7) =08(x+7)=0

STEP 6

olving the second equation for xxx gives usx+=0x + =0x+=0

STEP 7

Subtract7 from both sides to isolate xxx.x=−7x = -7x=−7So, the solutions to the equation x2+56x=0x^{2} +56x =0x2+56x=0 are x=0x =0x=0 and x=−7x = -7x=−7.Therefore, options C and D are correct.

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Studdy solves anything!

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

QuestionSolve $8 x^{2}+56 x=0$ and identify the correct solutions: A. $x=7$ , B. $x=8$ , C. $x=0$ , D. $x=-7$ .

Assumptions1. We are given the quadratic equation $8x^{} +56x =0$ . We are looking for the solutions to this equation, i.e., the values of $x$ that make the equation true.

The first step in solving a quadratic equation is to set the equation to zero. In this case, the equation is already set to zero.
$8x^{2} +56x =0$

Next, we can simplify the equation by factoring out the greatest common factor from the left side of the equation. $x(8x +56) =0$

We can further simplify the equation by factoring out8 from the term in the parentheses.
$x(8(x +7)) =0$

Now we have a product of two terms equal to zero. According to the zero product property, if a product of factors is zero, then at least one of the factors must be zero.
So, we can set each factor equal to zero and solve for $x$ .
$x =0$ $8(x +7) =0$

olving the second equation for $x$ gives us $x + =0$

Subtract7 from both sides to isolate $x$ .
$x = -7$ So, the solutions to the equation $x^{2} +56x =0$ are $x =0$ and $x = -7$ .
Therefore, options C and D are correct.