Basic Math Examples

${(y - 2)}^{2} = 11$

Step 1

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

$y - 2 = \pm \sqrt{11}$

Step 2

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

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Step 2.1

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

$y - 2 = \sqrt{11}$

Step 2.2

Add $2$ to both sides of the equation.

$y = \sqrt{11} + 2$

Step 2.3

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

$y - 2 = - \sqrt{11}$

Step 2.4

Add $2$ to both sides of the equation.

$y = - \sqrt{11} + 2$

Step 2.5

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

$y = \sqrt{11} + 2, - \sqrt{11} + 2$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \sqrt{11} + 2, - \sqrt{11} + 2$

Decimal Form:

$y = 5.31662479 \dots, - 1.31662479 \dots$