Solve for x x^2+(( square root of 3)/2)^2=1

$x^{2} + {(\frac{\sqrt{3}}{2})}^{2} = 1$

Simplify each term.

Apply the product rule to $\frac{\sqrt{3}}{2}$ .

$x^{2} + \frac{{\sqrt{3}}^{2}}{2^{2}} = 1$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$x^{2} + \frac{{(3^{\frac{1}{2}})}^{2}}{2^{2}} = 1$

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

$x^{2} + \frac{3^{\frac{1}{2} \cdot 2}}{2^{2}} = 1$

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

$x^{2} + \frac{3^{\frac{2}{2}}}{2^{2}} = 1$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{2} + \frac{3^{\frac{2}{2}}}{2^{2}} = 1$

Rewrite the expression.

$x^{2} + \frac{3^{1}}{2^{2}} = 1$

Evaluate the exponent.

$x^{2} + \frac{3}{2^{2}} = 1$

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

$x^{2} + \frac{3}{4} = 1$

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

Subtract $\frac{3}{4}$ from both sides of the equation.

$x^{2} = 1 - \frac{3}{4}$

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

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

Combine the numerators over the common denominator.

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

Subtract $3$ from $4$ .

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

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

$x = \pm \sqrt{\frac{1}{4}}$

Simplify $\pm \sqrt{\frac{1}{4}}$ .

Rewrite $\sqrt{\frac{1}{4}}$ as $\frac{\sqrt{1}}{\sqrt{4}}$ .

$x = \pm \frac{\sqrt{1}}{\sqrt{4}}$

Any root of $1$ is $1$ .

$x = \pm \frac{1}{\sqrt{4}}$

Simplify the denominator.

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

$x = \pm \frac{1}{\sqrt{2^{2}}}$

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

$x = \pm \frac{1}{2}$

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.

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

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

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

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

$x = \frac{1}{2}, - \frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}, - \frac{1}{2}$

Decimal Form:

$x = 0.5, - 0.5$

Solve for x x^2+(( square root of 3)/2)^2=1

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