Find the Roots (Zeros) square root of x+8=x+6

$\sqrt{x + 8} = x + 6$

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

${\sqrt{x + 8}}^{2} = {(x + 6)}^{2}$

Simplify each side of the equation.

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

${({(x + 8)}^{\frac{1}{2}})}^{2} = {(x + 6)}^{2}$

Simplify the left side.

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

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

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

${(x + 8)}^{\frac{1}{2} \cdot 2} = {(x + 6)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x + 8)}^{\frac{1}{2} \cdot 2} = {(x + 6)}^{2}$

Rewrite the expression.

${(x + 8)}^{1} = {(x + 6)}^{2}$

Simplify.

$x + 8 = {(x + 6)}^{2}$

Simplify the right side.

Simplify ${(x + 6)}^{2}$ .

Rewrite ${(x + 6)}^{2}$ as $(x + 6) (x + 6)$ .

$x + 8 = (x + 6) (x + 6)$

Expand $(x + 6) (x + 6)$ using the FOIL Method.

Apply the distributive property.

$x + 8 = x (x + 6) + 6 (x + 6)$

Apply the distributive property.

$x + 8 = x \cdot x + x \cdot 6 + 6 (x + 6)$

Apply the distributive property.

$x + 8 = x \cdot x + x \cdot 6 + 6 x + 6 \cdot 6$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x + 8 = x^{2} + x \cdot 6 + 6 x + 6 \cdot 6$

Move $6$ to the left of $x$ .

$x + 8 = x^{2} + 6 \cdot x + 6 x + 6 \cdot 6$

Multiply $6$ by $6$ .

$x + 8 = x^{2} + 6 x + 6 x + 36$

Add $6 x$ and $6 x$ .

$x + 8 = x^{2} + 12 x + 36$

Solve for $x$ .

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x^{2} + 12 x + 36 = x + 8$

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$x^{2} + 12 x + 36 - x = 8$

Subtract $x$ from $12 x$ .

$x^{2} + 11 x + 36 = 8$

Subtract $8$ from both sides of the equation.

$x^{2} + 11 x + 36 - 8 = 0$

Subtract $8$ from $36$ .

$x^{2} + 11 x + 28 = 0$

Factor $x^{2} + 11 x + 28$ 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 $28$ and whose sum is $11$ .

$4, 7$

Write the factored form using these integers.

$(x + 4) (x + 7) = 0$

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

$x + 4 = 0$

$x + 7 = 0$

Set $x + 4$ equal to $0$ and solve for $x$ .

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

Set $x + 7$ equal to $0$ and solve for $x$ .

Set $x + 7$ equal to $0$ .

$x + 7 = 0$

Subtract $7$ from both sides of the equation.

$x = - 7$

The final solution is all the values that make $(x + 4) (x + 7) = 0$ true.

$x = - 4, - 7$

Exclude the solutions that do not make $\sqrt{x + 8} = x + 6$ true.

$x = - 4$

Find the Roots (Zeros) square root of x+8=x+6

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