Solve for x 2 square root of 2x-3=-4

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

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

${(2 \sqrt{2 x - 3})}^{2} = {(- 4)}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x - 3}$ as ${(2 x - 3)}^{\frac{1}{2}}$ .

${(2 {(2 x - 3)}^{\frac{1}{2}})}^{2} = {(- 4)}^{2}$

Simplify the left side.

Simplify ${(2 {(2 x - 3)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $2 {(2 x - 3)}^{\frac{1}{2}}$ .

$2^{2} {({(2 x - 3)}^{\frac{1}{2}})}^{2} = {(- 4)}^{2}$

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

$4 {({(2 x - 3)}^{\frac{1}{2}})}^{2} = {(- 4)}^{2}$

Multiply the exponents in ${({(2 x - 3)}^{\frac{1}{2}})}^{2}$ .

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

$4 {(2 x - 3)}^{\frac{1}{2} \cdot 2} = {(- 4)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 {(2 x - 3)}^{\frac{1}{2} \cdot 2} = {(- 4)}^{2}$

Rewrite the expression.

$4 {(2 x - 3)}^{1} = {(- 4)}^{2}$

Simplify.

$4 (2 x - 3) = {(- 4)}^{2}$

Apply the distributive property.

$4 (2 x) + 4 \cdot - 3 = {(- 4)}^{2}$

Multiply.

Multiply $2$ by $4$ .

$8 x + 4 \cdot - 3 = {(- 4)}^{2}$

Multiply $4$ by $- 3$ .

$8 x - 12 = {(- 4)}^{2}$

Simplify the right side.

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

$8 x - 12 = 16$

Solve for $x$ .

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

Add $12$ to both sides of the equation.

$8 x = 16 + 12$

Add $16$ and $12$ .

$8 x = 28$

Divide each term in $8 x = 28$ by $8$ and simplify.

Divide each term in $8 x = 28$ by $8$ .

$\frac{8 x}{8} = \frac{28}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{28}{8}$

Divide $x$ by $1$ .

$x = \frac{28}{8}$

Simplify the right side.

Cancel the common factor of $28$ and $8$ .

Factor $4$ out of $28$ .

$x = \frac{4 (7)}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$x = \frac{4 \cdot 7}{4 \cdot 2}$

Cancel the common factor.

$x = \frac{4 \cdot 7}{4 \cdot 2}$

Rewrite the expression.

$x = \frac{7}{2}$

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

$No solution$

Solve for x 2 square root of 2x-3=-4

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