Question Solve the quadratic equation $49 m^{2} - 2 = 79$ for real-valued $m$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $49 m^{2} - 2 = 79$ .
2. We are to solve for the variable $m$ .

STEP 2

First, we need to isolate the term containing the variable $m$ on one side of the equation. To do this, we will add 2 to both sides of the equation to eliminate the constant term on the left side.
$49 m^{2} - 2 + 2 = 79 + 2$

STEP 3

Perform the addition on both sides of the equation.
$49 m^{2} = 81$

STEP 4

Next, we need to solve for $m^{2}$ . To do this, we will divide both sides of the equation by 49.
$\frac{49 m^{2}}{49} = \frac{81}{49}$

STEP 5

Perform the division to isolate $m^{2}$ .
$m^{2} = \frac{81}{49}$

STEP 6

Now, we need to take the square root of both sides of the equation to solve for $m$ . Since we are dealing with an equation, we must consider both the positive and negative square roots.
$m = \pm\sqrt{\frac{81}{49}}$

STEP 7

Calculate the square root of the fraction.
$m = \pm\frac{\sqrt{81}}{\sqrt{49}}$

STEP 8

Since both 81 and 49 are perfect squares, we can simplify the square roots.
$m = \pm\frac{9}{7}$

STEP 9

Thus, we have two solutions for $m$ .
$m = \frac{9}{7} \quad \text{or} \quad m = -\frac{9}{7}$
The solutions for the equation $49 m^{2} - 2 = 79$ are $m = \frac{9}{7}$ and $m = -\frac{9}{7}$ .

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Question Solve the quadratic equation $49 m^{2} - 2 = 79$ for real-valued $m$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $49 m^{2} - 2 = 79$ .
2. We are to solve for the variable $m$ .

STEP 2

First, we need to isolate the term containing the variable $m$ on one side of the equation. To do this, we will add 2 to both sides of the equation to eliminate the constant term on the left side.
$49 m^{2} - 2 + 2 = 79 + 2$

STEP 3

Perform the addition on both sides of the equation.
$49 m^{2} = 81$

STEP 4

Next, we need to solve for $m^{2}$ . To do this, we will divide both sides of the equation by 49.
$\frac{49 m^{2}}{49} = \frac{81}{49}$

STEP 5

Perform the division to isolate $m^{2}$ .
$m^{2} = \frac{81}{49}$

STEP 6

Now, we need to take the square root of both sides of the equation to solve for $m$ . Since we are dealing with an equation, we must consider both the positive and negative square roots.
$m = \pm\sqrt{\frac{81}{49}}$

STEP 7

Calculate the square root of the fraction.
$m = \pm\frac{\sqrt{81}}{\sqrt{49}}$

STEP 8

Since both 81 and 49 are perfect squares, we can simplify the square roots.
$m = \pm\frac{9}{7}$

STEP 9

Thus, we have two solutions for $m$ .
$m = \frac{9}{7} \quad \text{or} \quad m = -\frac{9}{7}$
The solutions for the equation $49 m^{2} - 2 = 79$ are $m = \frac{9}{7}$ and $m = -\frac{9}{7}$ .

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Question Solve the quadratic equation 49m2−2=7949 m^{2} - 2 = 7949m2−2=79 for real-valued mmm.

Studdy Solution

STEP 1

Assumptions1. We are given the equation 49m2−2=7949 m^{2} - 2 = 7949m2−2=79.2. We are to solve for the variable mmm.

STEP 2

First, we need to isolate the term containing the variable mmm on one side of the equation. To do this, we will add 2 to both sides of the equation to eliminate the constant term on the left side.49m2−2+2=79+249 m^{2} - 2 + 2 = 79 + 249m2−2+2=79+2

STEP 3

Perform the addition on both sides of the equation.49m2=8149 m^{2} = 8149m2=81

STEP 4

Next, we need to solve for m2m^{2}m2. To do this, we will divide both sides of the equation by 49.49m249=8149\frac{49 m^{2}}{49} = \frac{81}{49}4949m2​=4981​

STEP 5

Perform the division to isolate m2m^{2}m2.m2=8149m^{2} = \frac{81}{49}m2=4981​

STEP 6

Now, we need to take the square root of both sides of the equation to solve for mmm. Since we are dealing with an equation, we must consider both the positive and negative square roots.m=±8149m = \pm\sqrt{\frac{81}{49}}m=±4981​​

STEP 7

Calculate the square root of the fraction.m=±8149m = \pm\frac{\sqrt{81}}{\sqrt{49}}m=±49​81​​

STEP 8

Since both 81 and 49 are perfect squares, we can simplify the square roots.m=±97m = \pm\frac{9}{7}m=±79​

STEP 9

Thus, we have two solutions for mmm.m=97orm=−97m = \frac{9}{7} \quad \text{or} \quad m = -\frac{9}{7}m=79​orm=−79​The solutions for the equation 49m2−2=7949 m^{2} - 2 = 7949m2−2=79 are m=97m = \frac{9}{7}m=79​ and m=−97m = -\frac{9}{7}m=−79​.

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Question Solve the quadratic equation $49 m^{2} - 2 = 79$ for real-valued $m$ .

Assumptions
1. We are given the equation $49 m^{2} - 2 = 79$ .
2. We are to solve for the variable $m$ .

First, we need to isolate the term containing the variable $m$ on one side of the equation. To do this, we will add 2 to both sides of the equation to eliminate the constant term on the left side.
$49 m^{2} - 2 + 2 = 79 + 2$

Perform the addition on both sides of the equation.
$49 m^{2} = 81$

Next, we need to solve for $m^{2}$ . To do this, we will divide both sides of the equation by 49.
$\frac{49 m^{2}}{49} = \frac{81}{49}$

Perform the division to isolate $m^{2}$ .
$m^{2} = \frac{81}{49}$

Now, we need to take the square root of both sides of the equation to solve for $m$ . Since we are dealing with an equation, we must consider both the positive and negative square roots.
$m = \pm\sqrt{\frac{81}{49}}$

Calculate the square root of the fraction.
$m = \pm\frac{\sqrt{81}}{\sqrt{49}}$

Since both 81 and 49 are perfect squares, we can simplify the square roots.
$m = \pm\frac{9}{7}$

Thus, we have two solutions for $m$ .
$m = \frac{9}{7} \quad \text{or} \quad m = -\frac{9}{7}$
The solutions for the equation $49 m^{2} - 2 = 79$ are $m = \frac{9}{7}$ and $m = -\frac{9}{7}$ .