Algebra Examples

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

Step 1

Move all terms not containing $\sqrt{1 - x^{2}}$ to the right side of the equation.

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Step 1.1

Subtract $2$ from both sides of the equation.

$\sqrt{1 - x^{2}} = 3 - 2$

Step 1.2

Subtract $2$ from $3$ .

$\sqrt{1 - x^{2}} = 1$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{1 - x^{2}}}^{2} = 1^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(1 - x^{2})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(1 - x^{2})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

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

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

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

Step 3.2.1.1.2.2

Rewrite the expression.

${(1 - x^{2})}^{1} = 1^{2}$

Step 3.2.1.2

Simplify.

$1 - x^{2} = 1^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

One to any power is one.

$1 - x^{2} = 1$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $1$ from both sides of the equation.

$- x^{2} = 1 - 1$

Step 4.1.2

Subtract $1$ from $1$ .

$- x^{2} = 0$

Step 4.2

Divide each term in $- x^{2} = 0$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- x^{2} = 0$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{0}{- 1}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{0}{- 1}$

Step 4.2.2.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{0}{- 1}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $0$ by $- 1$ .

$x^{2} = 0$

Step 4.3

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

$x = \pm \sqrt{0}$

Step 4.4

Simplify $\pm \sqrt{0}$ .

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Step 4.4.1

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Step 4.4.2

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

$x = \pm 0$

Step 4.4.3

Plus or minus $0$ is $0$ .

$x = 0$