Solve for x (x+8)^2=(x-10)^(5/2)

${(x + 8)}^{2} = {(x - 10)}^{\frac{5}{2}}$

Simplify ${(x + 8)}^{2}$ .

Rewrite ${(x + 8)}^{2}$ as $(x + 8) (x + 8)$ .

$(x + 8) (x + 8) = {(x - 10)}^{\frac{5}{2}}$

Expand $(x + 8) (x + 8)$ using the FOIL Method.

Apply the distributive property.

$x (x + 8) + 8 (x + 8) = {(x - 10)}^{\frac{5}{2}}$

Apply the distributive property.

$x \cdot x + x \cdot 8 + 8 (x + 8) = {(x - 10)}^{\frac{5}{2}}$

Apply the distributive property.

$x \cdot x + x \cdot 8 + 8 x + 8 \cdot 8 = {(x - 10)}^{\frac{5}{2}}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 8 + 8 x + 8 \cdot 8 = {(x - 10)}^{\frac{5}{2}}$

Move $8$ to the left of $x$ .

$x^{2} + 8 \cdot x + 8 x + 8 \cdot 8 = {(x - 10)}^{\frac{5}{2}}$

Multiply $8$ by $8$ .

$x^{2} + 8 x + 8 x + 64 = {(x - 10)}^{\frac{5}{2}}$

Add $8 x$ and $8 x$ .

$x^{2} + 16 x + 64 = {(x - 10)}^{\frac{5}{2}}$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 27.31138411$