Basic Math Examples

${(y + 11)}^{2} = 49$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y + 11 = \pm \sqrt{49}$

Step 2

Simplify $\pm \sqrt{49}$ .

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Step 2.1

Rewrite $49$ as $7^{2}$ .

$y + 11 = \pm \sqrt{7^{2}}$

Step 2.2

Pull terms out from under the radical, assuming positive real numbers.

$y + 11 = \pm 7$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.1

First, use the positive value of the $\pm$ to find the first solution.

$y + 11 = 7$

Step 3.2

Move all terms not containing $y$ to the right side of the equation.

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Step 3.2.1

Subtract $11$ from both sides of the equation.

$y = 7 - 11$

Step 3.2.2

Subtract $11$ from $7$ .

$y = - 4$

Step 3.3

Next, use the negative value of the $\pm$ to find the second solution.

$y + 11 = - 7$

Step 3.4

Move all terms not containing $y$ to the right side of the equation.

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Step 3.4.1

Subtract $11$ from both sides of the equation.

$y = - 7 - 11$

Step 3.4.2

Subtract $11$ from $- 7$ .

$y = - 18$

Step 3.5

The complete solution is the result of both the positive and negative portions of the solution.

$y = - 4, - 18$