Solve for x -4 square root of x-6=-20

$- 4 \sqrt{x} - 6 = - 20$

Move all terms not containing $- 4 \sqrt{x}$ to the right side of the equation.

Add $6$ to both sides of the equation.

$- 4 \sqrt{x} = - 20 + 6$

Add $- 20$ and $6$ .

$- 4 \sqrt{x} = - 14$

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

${(- 4 \sqrt{x})}^{2} = {(- 14)}^{2}$

Simplify each side of the equation.

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

${(- 4 x^{\frac{1}{2}})}^{2} = {(- 14)}^{2}$

Simplify the left side.

Simplify ${(- 4 x^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $- 4 x^{\frac{1}{2}}$ .

${(- 4)}^{2} {(x^{\frac{1}{2}})}^{2} = {(- 14)}^{2}$

Raise $- 4$ to the power of $2$ .

$16 {(x^{\frac{1}{2}})}^{2} = {(- 14)}^{2}$

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

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

$16 x^{\frac{1}{2} \cdot 2} = {(- 14)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 x^{\frac{1}{2} \cdot 2} = {(- 14)}^{2}$

Rewrite the expression.

$16 x^{1} = {(- 14)}^{2}$

Simplify.

$16 x = {(- 14)}^{2}$

Simplify the right side.

Raise $- 14$ to the power of $2$ .

$16 x = 196$

Divide each term in $16 x = 196$ by $16$ and simplify.

Divide each term in $16 x = 196$ by $16$ .

$\frac{16 x}{16} = \frac{196}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x}{16} = \frac{196}{16}$

Divide $x$ by $1$ .

$x = \frac{196}{16}$

Simplify the right side.

Cancel the common factor of $196$ and $16$ .

Factor $4$ out of $196$ .

$x = \frac{4 (49)}{16}$

Cancel the common factors.

Factor $4$ out of $16$ .

$x = \frac{4 \cdot 49}{4 \cdot 4}$

Cancel the common factor.

$x = \frac{4 \cdot 49}{4 \cdot 4}$

Rewrite the expression.

$x = \frac{49}{4}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{49}{4}$

Decimal Form:

$x = 12.25$

Mixed Number Form:

$x = 12 \frac{1}{4}$

Solve for x -4 square root of x-6=-20

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