Solve for y 4 square root of 7-8y+3=15

$4 \sqrt{7 - 8 y} + 3 = 15$

Step 1

Move all terms not containing $4 \sqrt{7 - 8 y}$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$4 \sqrt{7 - 8 y} = 15 - 3$

Subtract $3$ from $15$ .

$4 \sqrt{7 - 8 y} = 12$

Step 2

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

${(4 \sqrt{7 - 8 y})}^{2} = 12^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 - 8 y}$ as ${(7 - 8 y)}^{\frac{1}{2}}$ .

${(4 {(7 - 8 y)}^{\frac{1}{2}})}^{2} = 12^{2}$

Simplify the left side.

Simplify ${(4 {(7 - 8 y)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $4 {(7 - 8 y)}^{\frac{1}{2}}$ .

$4^{2} {({(7 - 8 y)}^{\frac{1}{2}})}^{2} = 12^{2}$

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

$16 {({(7 - 8 y)}^{\frac{1}{2}})}^{2} = 12^{2}$

Multiply the exponents in ${({(7 - 8 y)}^{\frac{1}{2}})}^{2}$ .

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

$16 {(7 - 8 y)}^{\frac{1}{2} \cdot 2} = 12^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 {(7 - 8 y)}^{\frac{1}{2} \cdot 2} = 12^{2}$

Rewrite the expression.

$16 {(7 - 8 y)}^{1} = 12^{2}$

Simplify.

$16 (7 - 8 y) = 12^{2}$

Apply the distributive property.

$16 \cdot 7 + 16 (- 8 y) = 12^{2}$

Multiply.

Multiply $16$ by $7$ .

$112 + 16 (- 8 y) = 12^{2}$

Multiply $- 8$ by $16$ .

$112 - 128 y = 12^{2}$

Simplify the right side.

Raise $12$ to the power of $2$ .

$112 - 128 y = 144$

Step 4

Solve for $y$ .

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

Subtract $112$ from both sides of the equation.

$- 128 y = 144 - 112$

Subtract $112$ from $144$ .

$- 128 y = 32$

Divide each term in $- 128 y = 32$ by $- 128$ and simplify.

Divide each term in $- 128 y = 32$ by $- 128$ .

$\frac{- 128 y}{- 128} = \frac{32}{- 128}$

Simplify the left side.

Cancel the common factor of $- 128$ .

Cancel the common factor.

$\frac{- 128 y}{- 128} = \frac{32}{- 128}$

Divide $y$ by $1$ .

$y = \frac{32}{- 128}$

Simplify the right side.

Cancel the common factor of $32$ and $- 128$ .

Factor $32$ out of $32$ .

$y = \frac{32 (1)}{- 128}$

Cancel the common factors.

Factor $32$ out of $- 128$ .

$y = \frac{32 \cdot 1}{32 \cdot - 4}$

Cancel the common factor.

$y = \frac{32 \cdot 1}{32 \cdot - 4}$

Rewrite the expression.

$y = \frac{1}{- 4}$

Move the negative in front of the fraction.

$y = - \frac{1}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{1}{4}$

Decimal Form:

$y = - 0.25$

Solve for y 4 square root of 7-8y+3=15

Related Questions

Support LCMGCF.com by disabling your adblocker.