Solve for x (6x-7)^2+4=21

${(6 x - 7)}^{2} + 4 = 21$

Step 1

Subtract $4$ from both sides of the equation.

${(6 x - 7)}^{2} = 21 - 4$

Step 2

Subtract $4$ from $21$ .

${(6 x - 7)}^{2} = 17$

Step 3

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

$6 x - 7 = \pm \sqrt{17}$

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.

$6 x - 7 = \sqrt{17}$

Add $7$ to both sides of the equation.

$6 x = \sqrt{17} + 7$

Divide each term in $6 x = \sqrt{17} + 7$ by $6$ and simplify.

Divide each term in $6 x = \sqrt{17} + 7$ by $6$ .

$\frac{6 x}{6} = \frac{\sqrt{17}}{6} + \frac{7}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{\sqrt{17}}{6} + \frac{7}{6}$

Divide $x$ by $1$ .

$x = \frac{\sqrt{17}}{6} + \frac{7}{6}$

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

$6 x - 7 = - \sqrt{17}$

Add $7$ to both sides of the equation.

$6 x = - \sqrt{17} + 7$

Divide each term in $6 x = - \sqrt{17} + 7$ by $6$ and simplify.

Divide each term in $6 x = - \sqrt{17} + 7$ by $6$ .

$\frac{6 x}{6} = \frac{- \sqrt{17}}{6} + \frac{7}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- \sqrt{17}}{6} + \frac{7}{6}$

Divide $x$ by $1$ .

$x = \frac{- \sqrt{17}}{6} + \frac{7}{6}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{\sqrt{17}}{6} + \frac{7}{6}$

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

$x = \frac{\sqrt{17}}{6} + \frac{7}{6}, - \frac{\sqrt{17}}{6} + \frac{7}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{17}}{6} + \frac{7}{6}, - \frac{\sqrt{17}}{6} + \frac{7}{6}$

Decimal Form:

$x = 1.85385093 \dots, 0.47948239 \dots$

Solve for x (6x-7)^2+4=21

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