Solve for x 4(6-4x)^2=49

$4 {(6 - 4 x)}^{2} = 49$

Step 1

Divide each term in $4 {(6 - 4 x)}^{2} = 49$ by $4$ and simplify.

Divide each term in $4 {(6 - 4 x)}^{2} = 49$ by $4$ .

$\frac{4 {(6 - 4 x)}^{2}}{4} = \frac{49}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 {(6 - 4 x)}^{2}}{4} = \frac{49}{4}$

Divide ${(6 - 4 x)}^{2}$ by $1$ .

${(6 - 4 x)}^{2} = \frac{49}{4}$

Step 2

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

$6 - 4 x = \pm \sqrt{\frac{49}{4}}$

Step 3

Simplify $\pm \sqrt{\frac{49}{4}}$ .

Rewrite $\sqrt{\frac{49}{4}}$ as $\frac{\sqrt{49}}{\sqrt{4}}$ .

$6 - 4 x = \pm \frac{\sqrt{49}}{\sqrt{4}}$

Simplify the numerator.

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

$6 - 4 x = \pm \frac{\sqrt{7^{2}}}{\sqrt{4}}$

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

$6 - 4 x = \pm \frac{7}{\sqrt{4}}$

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

$6 - 4 x = \pm \frac{7}{\sqrt{2^{2}}}$

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

$6 - 4 x = \pm \frac{7}{2}$

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.

$6 - 4 x = \frac{7}{2}$

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

Subtract $6$ from both sides of the equation.

$- 4 x = \frac{7}{2} - 6$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 4 x = \frac{7}{2} - 6 \cdot \frac{2}{2}$

Combine $- 6$ and $\frac{2}{2}$ .

$- 4 x = \frac{7}{2} + \frac{- 6 \cdot 2}{2}$

Combine the numerators over the common denominator.

$- 4 x = \frac{7 - 6 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 6$ by $2$ .

$- 4 x = \frac{7 - 12}{2}$

Subtract $12$ from $7$ .

$- 4 x = \frac{- 5}{2}$

Move the negative in front of the fraction.

$- 4 x = - \frac{5}{2}$

Divide each term in $- 4 x = - \frac{5}{2}$ by $- 4$ and simplify.

Divide each term in $- 4 x = - \frac{5}{2}$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- \frac{5}{2}}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- \frac{5}{2}}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- \frac{5}{2}}{- 4}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{5}{2} \cdot \frac{1}{- 4}$

Move the negative in front of the fraction.

$x = - \frac{5}{2} (- \frac{1}{4})$

Multiply $- \frac{5}{2} (- \frac{1}{4})$ .

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{5}{2}) \frac{1}{4}$

Multiply $\frac{5}{2}$ by $1$ .

$x = \frac{5}{2} \cdot \frac{1}{4}$

Multiply $\frac{5}{2}$ by $\frac{1}{4}$ .

$x = \frac{5}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{5}{8}$

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

$6 - 4 x = - \frac{7}{2}$

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

Subtract $6$ from both sides of the equation.

$- 4 x = - \frac{7}{2} - 6$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 4 x = - \frac{7}{2} - 6 \cdot \frac{2}{2}$

Combine $- 6$ and $\frac{2}{2}$ .

$- 4 x = - \frac{7}{2} + \frac{- 6 \cdot 2}{2}$

Combine the numerators over the common denominator.

$- 4 x = \frac{- 7 - 6 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 6$ by $2$ .

$- 4 x = \frac{- 7 - 12}{2}$

Subtract $12$ from $- 7$ .

$- 4 x = \frac{- 19}{2}$

Move the negative in front of the fraction.

$- 4 x = - \frac{19}{2}$

Divide each term in $- 4 x = - \frac{19}{2}$ by $- 4$ and simplify.

Divide each term in $- 4 x = - \frac{19}{2}$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- \frac{19}{2}}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- \frac{19}{2}}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- \frac{19}{2}}{- 4}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{19}{2} \cdot \frac{1}{- 4}$

Move the negative in front of the fraction.

$x = - \frac{19}{2} (- \frac{1}{4})$

Multiply $- \frac{19}{2} (- \frac{1}{4})$ .

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{19}{2}) \frac{1}{4}$

Multiply $\frac{19}{2}$ by $1$ .

$x = \frac{19}{2} \cdot \frac{1}{4}$

Multiply $\frac{19}{2}$ by $\frac{1}{4}$ .

$x = \frac{19}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{19}{8}$

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

$x = \frac{5}{8}, \frac{19}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{8}, \frac{19}{8}$

Decimal Form:

$x = 0.625, 2.375$

Mixed Number Form:

$x = \frac{5}{8}, 2 \frac{3}{8}$

Solve for x 4(6-4x)^2=49

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