Solve for x x- square root of 9-8x=-18

$x - \sqrt{9 - 8 x} = - 18$

Step 1

Subtract $x$ from both sides of the equation.

$- \sqrt{9 - 8 x} = - 18 - x$

Step 2

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

${(- \sqrt{9 - 8 x})}^{2} = {(- 18 - x)}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{9 - 8 x}$ as ${(9 - 8 x)}^{\frac{1}{2}}$ .

${(- {(9 - 8 x)}^{\frac{1}{2}})}^{2} = {(- 18 - x)}^{2}$

Simplify the left side.

Simplify ${(- {(9 - 8 x)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $- {(9 - 8 x)}^{\frac{1}{2}}$ .

${(- 1)}^{2} {({(9 - 8 x)}^{\frac{1}{2}})}^{2} = {(- 18 - x)}^{2}$

Raise $- 1$ to the power of $2$ .

$1 {({(9 - 8 x)}^{\frac{1}{2}})}^{2} = {(- 18 - x)}^{2}$

Multiply ${({(9 - 8 x)}^{\frac{1}{2}})}^{2}$ by $1$ .

${({(9 - 8 x)}^{\frac{1}{2}})}^{2} = {(- 18 - x)}^{2}$

Multiply the exponents in ${({(9 - 8 x)}^{\frac{1}{2}})}^{2}$ .

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

${(9 - 8 x)}^{\frac{1}{2} \cdot 2} = {(- 18 - x)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(9 - 8 x)}^{\frac{1}{2} \cdot 2} = {(- 18 - x)}^{2}$

Rewrite the expression.

${(9 - 8 x)}^{1} = {(- 18 - x)}^{2}$

Simplify.

$9 - 8 x = {(- 18 - x)}^{2}$

Simplify the right side.

Simplify ${(- 18 - x)}^{2}$ .

Rewrite ${(- 18 - x)}^{2}$ as $(- 18 - x) (- 18 - x)$ .

$9 - 8 x = (- 18 - x) (- 18 - x)$

Expand $(- 18 - x) (- 18 - x)$ using the FOIL Method.

Apply the distributive property.

$9 - 8 x = - 18 (- 18 - x) - x (- 18 - x)$

Apply the distributive property.

$9 - 8 x = - 18 \cdot - 18 - 18 (- x) - x (- 18 - x)$

Apply the distributive property.

$9 - 8 x = - 18 \cdot - 18 - 18 (- x) - x \cdot - 18 - x (- x)$

Simplify and combine like terms.

Simplify each term.

Multiply $- 18$ by $- 18$ .

$9 - 8 x = 324 - 18 (- x) - x \cdot - 18 - x (- x)$

Multiply $- 1$ by $- 18$ .

$9 - 8 x = 324 + 18 x - x \cdot - 18 - x (- x)$

Multiply $- 18$ by $- 1$ .

$9 - 8 x = 324 + 18 x + 18 x - x (- x)$

Rewrite using the commutative property of multiplication.

$9 - 8 x = 324 + 18 x + 18 x - 1 \cdot - 1 x \cdot x$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$9 - 8 x = 324 + 18 x + 18 x - 1 \cdot - 1 (x \cdot x)$

Multiply $x$ by $x$ .

$9 - 8 x = 324 + 18 x + 18 x - 1 \cdot - 1 x^{2}$

Multiply $- 1$ by $- 1$ .

$9 - 8 x = 324 + 18 x + 18 x + 1 x^{2}$

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

$9 - 8 x = 324 + 18 x + 18 x + x^{2}$

Add $18 x$ and $18 x$ .

$9 - 8 x = 324 + 36 x + x^{2}$

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.

$324 + 36 x + x^{2} = 9 - 8 x$

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

Add $8 x$ to both sides of the equation.

$324 + 36 x + x^{2} + 8 x = 9$

Add $36 x$ and $8 x$ .

$324 + x^{2} + 44 x = 9$

Subtract $9$ from both sides of the equation.

$324 + x^{2} + 44 x - 9 = 0$

Subtract $9$ from $324$ .

$x^{2} + 44 x + 315 = 0$

Factor $x^{2} + 44 x + 315$ 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 $315$ and whose sum is $44$ .

$9, 35$

Write the factored form using these integers.

$(x + 9) (x + 35) = 0$

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

$x + 9 = 0$

$x + 35 = 0$

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.

$x = - 9$

Set $x + 35$ equal to $0$ and solve for $x$ .

Set $x + 35$ equal to $0$ .

$x + 35 = 0$

Subtract $35$ from both sides of the equation.

$x = - 35$

The final solution is all the values that make $(x + 9) (x + 35) = 0$ true.

$x = - 9, - 35$

Step 5

Exclude the solutions that do not make $x - \sqrt{9 - 8 x} = - 18$ true.

$x = - 9$

Solve for x x- square root of 9-8x=-18

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