Solve for x square root of x = square root of x-8-2

$\sqrt{x} = \sqrt{x - 8} - 2$

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

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

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$x^{1} = {(\sqrt{x - 8} - 2)}^{2}$

Simplify.

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

Simplify the right side.

Simplify ${(\sqrt{x - 8} - 2)}^{2}$ .

Rewrite ${(\sqrt{x - 8} - 2)}^{2}$ as $(\sqrt{x - 8} - 2) (\sqrt{x - 8} - 2)$ .

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

Expand $(\sqrt{x - 8} - 2) (\sqrt{x - 8} - 2)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

$x = \sqrt{x - 8} \sqrt{x - 8} + \sqrt{x - 8} \cdot - 2 - 2 (\sqrt{x - 8} - 2)$

Apply the distributive property.

$x = \sqrt{x - 8} \sqrt{x - 8} + \sqrt{x - 8} \cdot - 2 - 2 \sqrt{x - 8} - 2 \cdot - 2$

Simplify and combine like terms.

Simplify each term.

Multiply $\sqrt{x - 8} \sqrt{x - 8}$ .

Raise $\sqrt{x - 8}$ to the power of $1$ .

$x = {\sqrt{x - 8}}^{1} \sqrt{x - 8} + \sqrt{x - 8} \cdot - 2 - 2 \sqrt{x - 8} - 2 \cdot - 2$

Raise $\sqrt{x - 8}$ to the power of $1$ .

$x = {\sqrt{x - 8}}^{1} {\sqrt{x - 8}}^{1} + \sqrt{x - 8} \cdot - 2 - 2 \sqrt{x - 8} - 2 \cdot - 2$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = {\sqrt{x - 8}}^{1 + 1} + \sqrt{x - 8} \cdot - 2 - 2 \sqrt{x - 8} - 2 \cdot - 2$

Add $1$ and $1$ .

$x = {\sqrt{x - 8}}^{2} + \sqrt{x - 8} \cdot - 2 - 2 \sqrt{x - 8} - 2 \cdot - 2$

Rewrite ${\sqrt{x - 8}}^{2}$ as $x - 8$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x - 8}$ as ${(x - 8)}^{\frac{1}{2}}$ .

$x = {({(x - 8)}^{\frac{1}{2}})}^{2} + \sqrt{x - 8} \cdot - 2 - 2 \sqrt{x - 8} - 2 \cdot - 2$

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

$x = {(x - 8)}^{\frac{1}{2} \cdot 2} + \sqrt{x - 8} \cdot - 2 - 2 \sqrt{x - 8} - 2 \cdot - 2$

Combine $\frac{1}{2}$ and $2$ .

$x = {(x - 8)}^{\frac{2}{2}} + \sqrt{x - 8} \cdot - 2 - 2 \sqrt{x - 8} - 2 \cdot - 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = {(x - 8)}^{\frac{2}{2}} + \sqrt{x - 8} \cdot - 2 - 2 \sqrt{x - 8} - 2 \cdot - 2$

Rewrite the expression.

$x = {(x - 8)}^{1} + \sqrt{x - 8} \cdot - 2 - 2 \sqrt{x - 8} - 2 \cdot - 2$

Simplify.

$x = x - 8 + \sqrt{x - 8} \cdot - 2 - 2 \sqrt{x - 8} - 2 \cdot - 2$

Move $- 2$ to the left of $\sqrt{x - 8}$ .

$x = x - 8 - 2 \cdot \sqrt{x - 8} - 2 \sqrt{x - 8} - 2 \cdot - 2$

Multiply $- 2$ by $- 2$ .

$x = x - 8 - 2 \sqrt{x - 8} - 2 \sqrt{x - 8} + 4$

Add $- 8$ and $4$ .

$x = x - 4 - 2 \sqrt{x - 8} - 2 \sqrt{x - 8}$

Subtract $2 \sqrt{x - 8}$ from $- 2 \sqrt{x - 8}$ .

$x = x - 4 - 4 \sqrt{x - 8}$

Solve for $- 4 \sqrt{x - 8}$ .

Rewrite the equation as $x - 4 - 4 \sqrt{x - 8} = x$ .

$x - 4 - 4 \sqrt{x - 8} = x$

Move all terms not containing $- 4 \sqrt{x - 8}$ to the right side of the equation.

Subtract $x$ from both sides of the equation.

$- 4 - 4 \sqrt{x - 8} = x - x$

Add $4$ to both sides of the equation.

$- 4 \sqrt{x - 8} = x - x + 4$

Subtract $x$ from $x$ .

$- 4 \sqrt{x - 8} = 0 + 4$

Add $0$ and $4$ .

$- 4 \sqrt{x - 8} = 4$

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

${(- 4 \sqrt{x - 8})}^{2} = 4^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x - 8}$ as ${(x - 8)}^{\frac{1}{2}}$ .

${(- 4 {(x - 8)}^{\frac{1}{2}})}^{2} = 4^{2}$

Simplify the left side.

Simplify ${(- 4 {(x - 8)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $- 4 {(x - 8)}^{\frac{1}{2}}$ .

${(- 4)}^{2} {({(x - 8)}^{\frac{1}{2}})}^{2} = 4^{2}$

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

$16 {({(x - 8)}^{\frac{1}{2}})}^{2} = 4^{2}$

Multiply the exponents in ${({(x - 8)}^{\frac{1}{2}})}^{2}$ .

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

$16 {(x - 8)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 {(x - 8)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

$16 {(x - 8)}^{1} = 4^{2}$

Simplify.

$16 (x - 8) = 4^{2}$

Apply the distributive property.

$16 x + 16 \cdot - 8 = 4^{2}$

Multiply $16$ by $- 8$ .

$16 x - 128 = 4^{2}$

Simplify the right side.

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

$16 x - 128 = 16$

Solve for $x$ .

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

Add $128$ to both sides of the equation.

$16 x = 16 + 128$

Add $16$ and $128$ .

$16 x = 144$

Divide each term in $16 x = 144$ by $16$ and simplify.

Divide each term in $16 x = 144$ by $16$ .

$\frac{16 x}{16} = \frac{144}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x}{16} = \frac{144}{16}$

Divide $x$ by $1$ .

$x = \frac{144}{16}$

Simplify the right side.

Divide $144$ by $16$ .

$x = 9$

Exclude the solutions that do not make $\sqrt{x} = \sqrt{x - 8} - 2$ true.

$No solution$

Solve for x square root of x = square root of x-8-2

Related Questions

Support LCMGCF.com by disabling your adblocker.