Solve for p square root of p-4=-5

$\sqrt{p - 4} = - 5$

Step 1

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

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

Step 2

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$p - 4 = {(- 5)}^{2}$

Simplify the right side.

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

$p - 4 = 25$

Step 3

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

Add $4$ to both sides of the equation.

$p = 25 + 4$

Add $25$ and $4$ .

$p = 29$

Step 4

Exclude the solutions that do not make $\sqrt{p - 4} = - 5$ true.

$No solution$