Solve for x square root of 2x+26-9=x

$\sqrt{2 x + 26} - 9 = x$

Step 1

Add $9$ to both sides of the equation.

$\sqrt{2 x + 26} = x + 9$

Step 2

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

${\sqrt{2 x + 26}}^{2} = {(x + 9)}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x + 26}$ as ${(2 x + 26)}^{\frac{1}{2}}$ .

${({(2 x + 26)}^{\frac{1}{2}})}^{2} = {(x + 9)}^{2}$

Simplify the left side.

Simplify ${({(2 x + 26)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(2 x + 26)}^{\frac{1}{2}})}^{2}$ .

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

${(2 x + 26)}^{\frac{1}{2} \cdot 2} = {(x + 9)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 x + 26)}^{\frac{1}{2} \cdot 2} = {(x + 9)}^{2}$

Rewrite the expression.

${(2 x + 26)}^{1} = {(x + 9)}^{2}$

Simplify.

$2 x + 26 = {(x + 9)}^{2}$

Simplify the right side.

Simplify ${(x + 9)}^{2}$ .

Rewrite ${(x + 9)}^{2}$ as $(x + 9) (x + 9)$ .

$2 x + 26 = (x + 9) (x + 9)$

Expand $(x + 9) (x + 9)$ using the FOIL Method.

Apply the distributive property.

$2 x + 26 = x (x + 9) + 9 (x + 9)$

Apply the distributive property.

$2 x + 26 = x \cdot x + x \cdot 9 + 9 (x + 9)$

Apply the distributive property.

$2 x + 26 = x \cdot x + x \cdot 9 + 9 x + 9 \cdot 9$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$2 x + 26 = x^{2} + x \cdot 9 + 9 x + 9 \cdot 9$

Move $9$ to the left of $x$ .

$2 x + 26 = x^{2} + 9 \cdot x + 9 x + 9 \cdot 9$

Multiply $9$ by $9$ .

$2 x + 26 = x^{2} + 9 x + 9 x + 81$

Add $9 x$ and $9 x$ .

$2 x + 26 = x^{2} + 18 x + 81$

Step 4

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.

$x^{2} + 18 x + 81 = 2 x + 26$

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

Subtract $2 x$ from both sides of the equation.

$x^{2} + 18 x + 81 - 2 x = 26$

Subtract $2 x$ from $18 x$ .

$x^{2} + 16 x + 81 = 26$

Subtract $26$ from both sides of the equation.

$x^{2} + 16 x + 81 - 26 = 0$

Subtract $26$ from $81$ .

$x^{2} + 16 x + 55 = 0$

Factor $x^{2} + 16 x + 55$ 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 $55$ and whose sum is $16$ .

$5, 11$

Write the factored form using these integers.

$(x + 5) (x + 11) = 0$

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

$x + 5 = 0$

$x + 11 = 0$

Set $x + 5$ equal to $0$ and solve for $x$ .

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

Set $x + 11$ equal to $0$ and solve for $x$ .

Set $x + 11$ equal to $0$ .

$x + 11 = 0$

Subtract $11$ from both sides of the equation.

$x = - 11$

The final solution is all the values that make $(x + 5) (x + 11) = 0$ true.

$x = - 5, - 11$

Step 5

Exclude the solutions that do not make $\sqrt{2 x + 26} - 9 = x$ true.

$x = - 5$

Solve for x square root of 2x+26-9=x

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