Solve for x x^2+(1/2)^2=1^2

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

Step 1

Simplify each term.

Apply the product rule to $\frac{1}{2}$ .

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

One to any power is one.

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

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

$x^{2} + \frac{1}{4} = 1^{2}$

Step 2

One to any power is one.

$x^{2} + \frac{1}{4} = 1$

Step 3

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

Subtract $\frac{1}{4}$ from both sides of the equation.

$x^{2} = 1 - \frac{1}{4}$

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

$x^{2} = \frac{4}{4} - \frac{1}{4}$

Combine the numerators over the common denominator.

$x^{2} = \frac{4 - 1}{4}$

Subtract $1$ from $4$ .

$x^{2} = \frac{3}{4}$

Step 4

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

$x = \pm \sqrt{\frac{3}{4}}$

Step 5

Simplify $\pm \sqrt{\frac{3}{4}}$ .

Rewrite $\sqrt{\frac{3}{4}}$ as $\frac{\sqrt{3}}{\sqrt{4}}$ .

$x = \pm \frac{\sqrt{3}}{\sqrt{4}}$

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

$x = \pm \frac{\sqrt{3}}{\sqrt{2^{2}}}$

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

$x = \pm \frac{\sqrt{3}}{2}$

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.

$x = \frac{\sqrt{3}}{2}$

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

$x = - \frac{\sqrt{3}}{2}$

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

$x = \frac{\sqrt{3}}{2}, - \frac{\sqrt{3}}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{3}}{2}, - \frac{\sqrt{3}}{2}$

Decimal Form:

$x = 0.86602540 \dots, - 0.86602540 \dots$

Solve for x x^2+(1/2)^2=1^2

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