Evaluate 2 square root of 5x-4-3=-11

$2 \sqrt{5 x - 4} - 3 = - 11$

Move all terms not containing $2 \sqrt{5 x - 4}$ to the right side of the equation.

Add $3$ to both sides of the equation.

$2 \sqrt{5 x - 4} = - 11 + 3$

Add $- 11$ and $3$ .

$2 \sqrt{5 x - 4} = - 8$

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

${(2 \sqrt{5 x - 4})}^{2} = {(- 8)}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x - 4}$ as ${(5 x - 4)}^{\frac{1}{2}}$ .

${(2 {(5 x - 4)}^{\frac{1}{2}})}^{2} = {(- 8)}^{2}$

Simplify the left side.

Simplify ${(2 {(5 x - 4)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $2 {(5 x - 4)}^{\frac{1}{2}}$ .

$2^{2} {({(5 x - 4)}^{\frac{1}{2}})}^{2} = {(- 8)}^{2}$

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

$4 {({(5 x - 4)}^{\frac{1}{2}})}^{2} = {(- 8)}^{2}$

Multiply the exponents in ${({(5 x - 4)}^{\frac{1}{2}})}^{2}$ .

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

$4 {(5 x - 4)}^{\frac{1}{2} \cdot 2} = {(- 8)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 {(5 x - 4)}^{\frac{1}{2} \cdot 2} = {(- 8)}^{2}$

Rewrite the expression.

$4 {(5 x - 4)}^{1} = {(- 8)}^{2}$

Simplify.

$4 (5 x - 4) = {(- 8)}^{2}$

Apply the distributive property.

$4 (5 x) + 4 \cdot - 4 = {(- 8)}^{2}$

Multiply.

Multiply $5$ by $4$ .

$20 x + 4 \cdot - 4 = {(- 8)}^{2}$

Multiply $4$ by $- 4$ .

$20 x - 16 = {(- 8)}^{2}$

Simplify the right side.

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

$20 x - 16 = 64$

Solve for $x$ .

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

Add $16$ to both sides of the equation.

$20 x = 64 + 16$

Add $64$ and $16$ .

$20 x = 80$

Divide each term in $20 x = 80$ by $20$ and simplify.

Divide each term in $20 x = 80$ by $20$ .

$\frac{20 x}{20} = \frac{80}{20}$

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{20 x}{20} = \frac{80}{20}$

Divide $x$ by $1$ .

$x = \frac{80}{20}$

Simplify the right side.

Divide $80$ by $20$ .

$x = 4$

Exclude the solutions that do not make $2 \sqrt{5 x - 4} - 3 = - 11$ true.

$No solution$

Evaluate 2 square root of 5x-4-3=-11

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