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

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

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

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

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{12 - 5 x}$ as ${(12 - 5 x)}^{\frac{1}{2}}$ .

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

Simplify the left side.

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

Multiply the exponents in ${({(12 - 5 x)}^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Simplify ${(5 x)}^{2}$ .

Apply the product rule to $5 x$ .

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

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

$12 - 5 x = 25 x^{2}$

Solve for $x$ .

Subtract $25 x^{2}$ from both sides of the equation.

$12 - 5 x - 25 x^{2} = 0$

Factor the left side of the equation.

Factor $- 1$ out of $12 - 5 x - 25 x^{2}$ .

Reorder the expression.

Move $12$ .

$- 5 x - 25 x^{2} + 12 = 0$

Reorder $- 5 x$ and $- 25 x^{2}$ .

$- 25 x^{2} - 5 x + 12 = 0$

Factor $- 1$ out of $- 25 x^{2}$ .

$- (25 x^{2}) - 5 x + 12 = 0$

Factor $- 1$ out of $- 5 x$ .

$- (25 x^{2}) - (5 x) + 12 = 0$

Rewrite $12$ as $- 1 (- 12)$ .

$- (25 x^{2}) - (5 x) - 1 \cdot - 12 = 0$

Factor $- 1$ out of $- (25 x^{2}) - (5 x)$ .

$- (25 x^{2} + 5 x) - 1 \cdot - 12 = 0$

Factor $- 1$ out of $- (25 x^{2} + 5 x) - 1 (- 12)$ .

$- (25 x^{2} + 5 x - 12) = 0$

Factor.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 25 \cdot - 12 = - 300$ and whose sum is $b = 5$ .

Factor $5$ out of $5 x$ .

$- (25 x^{2} + 5 (x) - 12) = 0$

Rewrite $5$ as $- 15$ plus $20$

$- (25 x^{2} + (- 15 + 20) x - 12) = 0$

Apply the distributive property.

$- (25 x^{2} - 15 x + 20 x - 12) = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$- ((25 x^{2} - 15 x) + 20 x - 12) = 0$

Factor out the greatest common factor (GCF) from each group.

$- (5 x (5 x - 3) + 4 (5 x - 3)) = 0$

Factor the polynomial by factoring out the greatest common factor, $5 x - 3$ .

$- ((5 x - 3) (5 x + 4)) = 0$

Remove unnecessary parentheses.

$- (5 x - 3) (5 x + 4) = 0$

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

$5 x - 3 = 0$

$5 x + 4 = 0$

Set $5 x - 3$ equal to $0$ and solve for $x$ .

Set $5 x - 3$ equal to $0$ .

$5 x - 3 = 0$

Solve $5 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$5 x = 3$

Divide each term in $5 x = 3$ by $5$ and simplify.

Divide each term in $5 x = 3$ by $5$ .

$\frac{5 x}{5} = \frac{3}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{3}{5}$

Divide $x$ by $1$ .

$x = \frac{3}{5}$

Set $5 x + 4$ equal to $0$ and solve for $x$ .

Set $5 x + 4$ equal to $0$ .

$5 x + 4 = 0$

Solve $5 x + 4 = 0$ for $x$ .

Subtract $4$ from both sides of the equation.

$5 x = - 4$

Divide each term in $5 x = - 4$ by $5$ and simplify.

Divide each term in $5 x = - 4$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

The final solution is all the values that make $- (5 x - 3) (5 x + 4) = 0$ true.

$x = \frac{3}{5}, - \frac{4}{5}$

Exclude the solutions that do not make $\sqrt{12 - 5 x} = 5 x$ true.

$x = \frac{3}{5}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{5}$

Decimal Form:

$x = 0.6$

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

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