Solve for x square root of x^2+4-1=2

$\sqrt{x^{2} + 4} - 1 = 2$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x^{2} + 4}$ as ${(x^{2} + 4)}^{\frac{1}{2}}$ .

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

Step 2

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

Add $1$ to both sides of the equation.

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

Add $2$ and $1$ .

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

Step 3

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

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

Step 4

Simplify the exponent.

Simplify the left side.

Simplify ${({(x^{2} + 4)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(x^{2} + 4)}^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

${(x^{2} + 4)}^{1} = 3^{2}$

Simplify.

$x^{2} + 4 = 3^{2}$

Simplify the right side.

Raise $3$ to the power of $2$ .

$x^{2} + 4 = 9$

Step 5

Solve for $x$ .

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

Subtract $4$ from both sides of the equation.

$x^{2} = 9 - 4$

Subtract $4$ from $9$ .

$x^{2} = 5$

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

$x = \pm \sqrt{5}$

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.

$x = \sqrt{5}$

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

$x = - \sqrt{5}$

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

$x = \sqrt{5}, - \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{5}, - \sqrt{5}$

Decimal Form:

$x = 2.23606797 \dots, - 2.23606797 \dots$

Solve for x square root of x^2+4-1=2

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