Solve for x square root of x^2+8x=3

$\sqrt{x^{2} + 8 x} = 3$

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

${\sqrt{x^{2} + 8 x}}^{2} = 3^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x^{2} + 8 x}$ as ${(x^{2} + 8 x)}^{\frac{1}{2}}$ .

${({(x^{2} + 8 x)}^{\frac{1}{2}})}^{2} = 3^{2}$

Simplify the left side.

Simplify ${({(x^{2} + 8 x)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(x^{2} + 8 x)}^{\frac{1}{2}})}^{2}$ .

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

${(x^{2} + 8 x)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x^{2} + 8 x)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

${(x^{2} + 8 x)}^{1} = 3^{2}$

Simplify.

$x^{2} + 8 x = 3^{2}$

Simplify the right side.

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

$x^{2} + 8 x = 9$

Solve for $x$ .

Subtract $9$ from both sides of the equation.

$x^{2} + 8 x - 9 = 0$

Factor $x^{2} + 8 x - 9$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 9$ and whose sum is $8$ .

$- 1, 9$

Write the factored form using these integers.

$(x - 1) (x + 9) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 1 = 0$

$x + 9 = 0$

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Set $x + 9$ equal to $0$ and solve for $x$ .

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

Subtract $9$ from both sides of the equation.

$x = - 9$

The final solution is all the values that make $(x - 1) (x + 9) = 0$ true.

$x = 1, - 9$

Solve for x square root of x^2+8x=3

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