Solve for x 12-7 square root of x-5=4

$12 - 7 \sqrt{x - 5} = 4$

Move all terms not containing $- 7 \sqrt{x - 5}$ to the right side of the equation.

Subtract $12$ from both sides of the equation.

$- 7 \sqrt{x - 5} = 4 - 12$

Subtract $12$ from $4$ .

$- 7 \sqrt{x - 5} = - 8$

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

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

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x - 5}$ as ${(x - 5)}^{\frac{1}{2}}$ .

${(- 7 {(x - 5)}^{\frac{1}{2}})}^{2} = {(- 8)}^{2}$

Simplify the left side.

Simplify ${(- 7 {(x - 5)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $- 7 {(x - 5)}^{\frac{1}{2}}$ .

${(- 7)}^{2} {({(x - 5)}^{\frac{1}{2}})}^{2} = {(- 8)}^{2}$

Raise $- 7$ to the power of $2$ .

$49 {({(x - 5)}^{\frac{1}{2}})}^{2} = {(- 8)}^{2}$

Multiply the exponents in ${({(x - 5)}^{\frac{1}{2}})}^{2}$ .

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

$49 {(x - 5)}^{\frac{1}{2} \cdot 2} = {(- 8)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$49 {(x - 5)}^{\frac{1}{2} \cdot 2} = {(- 8)}^{2}$

Rewrite the expression.

$49 {(x - 5)}^{1} = {(- 8)}^{2}$

Simplify.

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

Apply the distributive property.

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

Multiply $49$ by $- 5$ .

$49 x - 245 = {(- 8)}^{2}$

Simplify the right side.

Raise $- 8$ to the power of $2$ .

$49 x - 245 = 64$

Solve for $x$ .

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

Add $245$ to both sides of the equation.

$49 x = 64 + 245$

Add $64$ and $245$ .

$49 x = 309$

Divide each term in $49 x = 309$ by $49$ and simplify.

Divide each term in $49 x = 309$ by $49$ .

$\frac{49 x}{49} = \frac{309}{49}$

Simplify the left side.

Cancel the common factor of $49$ .

Cancel the common factor.

$\frac{49 x}{49} = \frac{309}{49}$

Divide $x$ by $1$ .

$x = \frac{309}{49}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{309}{49}$

Decimal Form:

$x = 6.30612244 \dots$

Mixed Number Form:

$x = 6 \frac{15}{49}$

Solve for x 12-7 square root of x-5=4

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