Algebra Examples

$g (x) = {(x - 5)}^{2} + 2 x^{3}$

Step 1

Set ${(x - 5)}^{2} + 2 x^{3}$ equal to $0$ .

${(x - 5)}^{2} + 2 x^{3} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite ${(x - 5)}^{2}$ as $(x - 5) (x - 5)$ .

$(x - 5) (x - 5) + 2 x^{3} = 0$

Step 2.1.2

Expand $(x - 5) (x - 5)$ using the FOIL Method.

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Step 2.1.2.1

Apply the distributive property.

$x (x - 5) - 5 (x - 5) + 2 x^{3} = 0$

Step 2.1.2.2

Apply the distributive property.

$x \cdot x + x \cdot - 5 - 5 (x - 5) + 2 x^{3} = 0$

Step 2.1.2.3

Apply the distributive property.

$x \cdot x + x \cdot - 5 - 5 x - 5 \cdot - 5 + 2 x^{3} = 0$

Step 2.1.3

Simplify and combine like terms.

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Step 2.1.3.1

Simplify each term.

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Step 2.1.3.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 5 - 5 x - 5 \cdot - 5 + 2 x^{3} = 0$

Step 2.1.3.1.2

Move $- 5$ to the left of $x$ .

$x^{2} - 5 \cdot x - 5 x - 5 \cdot - 5 + 2 x^{3} = 0$

Step 2.1.3.1.3

Multiply $- 5$ by $- 5$ .

$x^{2} - 5 x - 5 x + 25 + 2 x^{3} = 0$

Step 2.1.3.2

Subtract $5 x$ from $- 5 x$ .

$x^{2} - 10 x + 25 + 2 x^{3} = 0$

Step 2.2

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

$x \approx - 3.23726945$

Step 3