Solve by Factoring fifth root of x^2-12x=-2

$\sqrt[5]{x^{2} - 12 x} = - 2$

Step 1

Add $2$ to both sides of the equation.

$\sqrt[5]{x^{2} - 12 x} + 2 = 0$

Step 2

Factor $x$ out of $x^{2} - 12 x$ .

Factor $x$ out of $x^{2}$ .

$\sqrt[5]{x \cdot x - 12 x} + 2 = 0$

Factor $x$ out of $- 12 x$ .

$\sqrt[5]{x \cdot x + x \cdot - 12} + 2 = 0$

Factor $x$ out of $x \cdot x + x \cdot - 12$ .

$\sqrt[5]{x (x - 12)} + 2 = 0$

Step 3

Subtract $2$ from both sides of the equation.

$\sqrt[5]{x (x - 12)} = - 2$

Step 4

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $5$ .

${\sqrt[5]{x (x - 12)}}^{5} = {(- 2)}^{5}$

Step 5

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{x (x - 12)}$ as ${(x (x - 12))}^{\frac{1}{5}}$ .

${({(x (x - 12))}^{\frac{1}{5}})}^{5} = {(- 2)}^{5}$

Simplify the left side.

Simplify ${({(x (x - 12))}^{\frac{1}{5}})}^{5}$ .

Multiply the exponents in ${({(x (x - 12))}^{\frac{1}{5}})}^{5}$ .

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

${(x (x - 12))}^{\frac{1}{5} \cdot 5} = {(- 2)}^{5}$

Cancel the common factor of $5$ .

Cancel the common factor.

${(x (x - 12))}^{\frac{1}{5} \cdot 5} = {(- 2)}^{5}$

Rewrite the expression.

${(x (x - 12))}^{1} = {(- 2)}^{5}$

Apply the distributive property.

${(x \cdot x + x \cdot - 12)}^{1} = {(- 2)}^{5}$

Simplify the expression.

Multiply $x$ by $x$ .

${(x^{2} + x \cdot - 12)}^{1} = {(- 2)}^{5}$

Move $- 12$ to the left of $x$ .

$x^{2} - 12 x = {(- 2)}^{5}$

Simplify the right side.

Raise $- 2$ to the power of $5$ .

$x^{2} - 12 x = - 32$

Step 6

Solve for $x$ .

Add $32$ to both sides of the equation.

$x^{2} - 12 x + 32 = 0$

Factor $x^{2} - 12 x + 32$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $32$ and whose sum is $- 12$ .

$- 8, - 4$

Write the factored form using these integers.

$(x - 8) (x - 4) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 8 = 0$

$x - 4 = 0$

Set $x - 8$ equal to $0$ and solve for $x$ .

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

The final solution is all the values that make $(x - 8) (x - 4) = 0$ true.

$x = 8, 4$

Solve by Factoring fifth root of x^2-12x=-2

Related Questions

Support LCMGCF.com by disabling your adblocker.