Solve for x x^2+(-( square root of 11)/6)^2=1^2

$x^{2} + {(- \frac{\sqrt{11}}{6})}^{2} = 1^{2}$

Step 1

Simplify each term.

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{\sqrt{11}}{6}$ .

$x^{2} + {(- 1)}^{2} {(\frac{\sqrt{11}}{6})}^{2} = 1^{2}$

Apply the product rule to $\frac{\sqrt{11}}{6}$ .

$x^{2} + {(- 1)}^{2} \frac{{\sqrt{11}}^{2}}{6^{2}} = 1^{2}$

Raise $- 1$ to the power of $2$ .

$x^{2} + 1 \frac{{\sqrt{11}}^{2}}{6^{2}} = 1^{2}$

Multiply $\frac{{\sqrt{11}}^{2}}{6^{2}}$ by $1$ .

$x^{2} + \frac{{\sqrt{11}}^{2}}{6^{2}} = 1^{2}$

Rewrite ${\sqrt{11}}^{2}$ as $11$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{11}$ as $11^{\frac{1}{2}}$ .

$x^{2} + \frac{{(11^{\frac{1}{2}})}^{2}}{6^{2}} = 1^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{2} + \frac{11^{\frac{1}{2} \cdot 2}}{6^{2}} = 1^{2}$

Combine $\frac{1}{2}$ and $2$ .

$x^{2} + \frac{11^{\frac{2}{2}}}{6^{2}} = 1^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{2} + \frac{11^{\frac{2}{2}}}{6^{2}} = 1^{2}$

Rewrite the expression.

$x^{2} + \frac{11^{1}}{6^{2}} = 1^{2}$

Evaluate the exponent.

$x^{2} + \frac{11}{6^{2}} = 1^{2}$

Raise $6$ to the power of $2$ .

$x^{2} + \frac{11}{36} = 1^{2}$

Step 2

One to any power is one.

$x^{2} + \frac{11}{36} = 1$

Step 3

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

Subtract $\frac{11}{36}$ from both sides of the equation.

$x^{2} = 1 - \frac{11}{36}$

Write $1$ as a fraction with a common denominator.

$x^{2} = \frac{36}{36} - \frac{11}{36}$

Combine the numerators over the common denominator.

$x^{2} = \frac{36 - 11}{36}$

Subtract $11$ from $36$ .

$x^{2} = \frac{25}{36}$

Step 4

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

$x = \pm \sqrt{\frac{25}{36}}$

Step 5

Simplify $\pm \sqrt{\frac{25}{36}}$ .

Rewrite $\sqrt{\frac{25}{36}}$ as $\frac{\sqrt{25}}{\sqrt{36}}$ .

$x = \pm \frac{\sqrt{25}}{\sqrt{36}}$

Simplify the numerator.

Rewrite $25$ as $5^{2}$ .

$x = \pm \frac{\sqrt{5^{2}}}{\sqrt{36}}$

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

$x = \pm \frac{5}{\sqrt{36}}$

Simplify the denominator.

Rewrite $36$ as $6^{2}$ .

$x = \pm \frac{5}{\sqrt{6^{2}}}$

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

$x = \pm \frac{5}{6}$

Step 6

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

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

$x = \frac{5}{6}$

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

$x = - \frac{5}{6}$

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

$x = \frac{5}{6}, - \frac{5}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{6}, - \frac{5}{6}$

Decimal Form:

$x = 0.8\overline{3}, - 0.8\overline{3}$

Solve for x x^2+(-( square root of 11)/6)^2=1^2

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