Solve for x (5x+8)^2-8=35

${(5 x + 8)}^{2} - 8 = 35$

Step 1

Add $8$ to both sides of the equation.

${(5 x + 8)}^{2} = 35 + 8$

Step 2

Add $35$ and $8$ .

${(5 x + 8)}^{2} = 43$

Step 3

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

$5 x + 8 = \pm \sqrt{43}$

Step 4

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.

$5 x + 8 = \sqrt{43}$

Subtract $8$ from both sides of the equation.

$5 x = \sqrt{43} - 8$

Divide each term in $5 x = \sqrt{43} - 8$ by $5$ and simplify.

Divide each term in $5 x = \sqrt{43} - 8$ by $5$ .

$\frac{5 x}{5} = \frac{\sqrt{43}}{5} + \frac{- 8}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{\sqrt{43}}{5} + \frac{- 8}{5}$

Divide $x$ by $1$ .

$x = \frac{\sqrt{43}}{5} + \frac{- 8}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{\sqrt{43}}{5} - \frac{8}{5}$

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

$5 x + 8 = - \sqrt{43}$

Subtract $8$ from both sides of the equation.

$5 x = - \sqrt{43} - 8$

Divide each term in $5 x = - \sqrt{43} - 8$ by $5$ and simplify.

Divide each term in $5 x = - \sqrt{43} - 8$ by $5$ .

$\frac{5 x}{5} = \frac{- \sqrt{43}}{5} + \frac{- 8}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- \sqrt{43}}{5} + \frac{- 8}{5}$

Divide $x$ by $1$ .

$x = \frac{- \sqrt{43}}{5} + \frac{- 8}{5}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{\sqrt{43}}{5} + \frac{- 8}{5}$

Move the negative in front of the fraction.

$x = - \frac{\sqrt{43}}{5} - \frac{8}{5}$

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

$x = \frac{\sqrt{43}}{5} - \frac{8}{5}, - \frac{\sqrt{43}}{5} - \frac{8}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{43}}{5} - \frac{8}{5}, - \frac{\sqrt{43}}{5} - \frac{8}{5}$

Decimal Form:

$x = - 0.28851229 \dots, - 2.91148770 \dots$

Solve for x (5x+8)^2-8=35

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