Solve Using the Square Root Property (5x-8)^2=49

${(5 x - 8)}^{2} = 49$

Step 1

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

$5 x - 8 = \pm \sqrt{49}$

Step 2

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

$5 x - 8 = \pm \sqrt{7^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$5 x - 8 = \pm 7$

Step 3

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.

$5 x - 8 = 7$

Move all terms not containing $x$ to the right side of the equation.

Add $8$ to both sides of the equation.

$5 x = 7 + 8$

Add $7$ and $8$ .

$5 x = 15$

Divide each term in $5 x = 15$ by $5$ and simplify.

Divide each term in $5 x = 15$ by $5$ .

$\frac{5 x}{5} = \frac{15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{15}{5}$

Divide $x$ by $1$ .

$x = \frac{15}{5}$

Simplify the right side.

Divide $15$ by $5$ .

$x = 3$

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

$5 x - 8 = - 7$

Move all terms not containing $x$ to the right side of the equation.

Add $8$ to both sides of the equation.

$5 x = - 7 + 8$

Add $- 7$ and $8$ .

$5 x = 1$

Divide each term in $5 x = 1$ by $5$ and simplify.

Divide each term in $5 x = 1$ by $5$ .

$\frac{5 x}{5} = \frac{1}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{1}{5}$

Divide $x$ by $1$ .

$x = \frac{1}{5}$

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

$x = 3, \frac{1}{5}$

Solve Using the Square Root Property (5x-8)^2=49

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