Solve for z -10 = cube root of 2(1.25)+z-12

$- 10 = \sqrt[3]{2 (1.25) + z} - 12$

Rewrite the equation as $\sqrt[3]{2 (1.25) + z} - 12 = - 10$ .

$\sqrt[3]{2 (1.25) + z} - 12 = - 10$

Move all terms not containing $\sqrt[3]{2 (1.25) + z}$ to the right side of the equation.

Add $12$ to both sides of the equation.

$\sqrt[3]{2 (1.25) + z} = - 10 + 12$

Add $- 10$ and $12$ .

$\sqrt[3]{2 (1.25) + z} = 2$

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

${\sqrt[3]{2 (1.25) + z}}^{3} = 2^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 (1.25) + z}$ as ${(2 (1.25) + z)}^{\frac{1}{3}}$ .

${({(2 (1.25) + z)}^{\frac{1}{3}})}^{3} = 2^{3}$

Simplify the left side.

Simplify ${({(2 (1.25) + z)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(2 (1.25) + z)}^{\frac{1}{3}})}^{3}$ .

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

${(2 (1.25) + z)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(2 (1.25) + z)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Rewrite the expression.

${(2 (1.25) + z)}^{1} = 2^{3}$

Multiply $2$ by $1.25$ .

${(2.5 + z)}^{1} = 2^{3}$

Simplify.

$2.5 + z = 2^{3}$

Simplify the right side.

Raise $2$ to the power of $3$ .

$2.5 + z = 8$

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

Subtract $2.5$ from both sides of the equation.

$z = 8 - 2.5$

Subtract $2.5$ from $8$ .

$z = 5.5$