Solve for p 7 square root of 1-9p=56

$7 \sqrt{1 - 9 p} = 56$

Step 1

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

${(7 \sqrt{1 - 9 p})}^{2} = 56^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{1 - 9 p}$ as ${(1 - 9 p)}^{\frac{1}{2}}$ .

${(7 {(1 - 9 p)}^{\frac{1}{2}})}^{2} = 56^{2}$

Simplify the left side.

Simplify ${(7 {(1 - 9 p)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $7 {(1 - 9 p)}^{\frac{1}{2}}$ .

$7^{2} {({(1 - 9 p)}^{\frac{1}{2}})}^{2} = 56^{2}$

Raise $7$ to the power of $2$ .

$49 {({(1 - 9 p)}^{\frac{1}{2}})}^{2} = 56^{2}$

Multiply the exponents in ${({(1 - 9 p)}^{\frac{1}{2}})}^{2}$ .

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

$49 {(1 - 9 p)}^{\frac{1}{2} \cdot 2} = 56^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$49 {(1 - 9 p)}^{\frac{1}{2} \cdot 2} = 56^{2}$

Rewrite the expression.

$49 {(1 - 9 p)}^{1} = 56^{2}$

Simplify.

$49 (1 - 9 p) = 56^{2}$

Apply the distributive property.

$49 \cdot 1 + 49 (- 9 p) = 56^{2}$

Multiply.

Multiply $49$ by $1$ .

$49 + 49 (- 9 p) = 56^{2}$

Multiply $- 9$ by $49$ .

$49 - 441 p = 56^{2}$

Simplify the right side.

Raise $56$ to the power of $2$ .

$49 - 441 p = 3136$

Step 3

Solve for $p$ .

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

Subtract $49$ from both sides of the equation.

$- 441 p = 3136 - 49$

Subtract $49$ from $3136$ .

$- 441 p = 3087$

Divide each term in $- 441 p = 3087$ by $- 441$ and simplify.

Divide each term in $- 441 p = 3087$ by $- 441$ .

$\frac{- 441 p}{- 441} = \frac{3087}{- 441}$

Simplify the left side.

Cancel the common factor of $- 441$ .

Cancel the common factor.

$\frac{- 441 p}{- 441} = \frac{3087}{- 441}$

Divide $p$ by $1$ .

$p = \frac{3087}{- 441}$

Simplify the right side.

Divide $3087$ by $- 441$ .

$p = - 7$

Solve for p 7 square root of 1-9p=56

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