Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $x$ by $x$ .

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

Step 1.3.1.2

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

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

Step 1.3.1.3

Multiply $8$ by $8$ .

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

Step 1.3.2

Add $8 x$ and $8 x$ .

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

Step 2

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

$x \approx 27.31138411$

Step 3