Algebra Examples

${(x + 3)}^{4} = 362$

Step 1

Subtract $362$ from both sides of the equation.

${(x + 3)}^{4} - 362 = 0$

Step 2

Simplify ${(x + 3)}^{4} - 362$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Use the Binomial Theorem.

$x^{4} + 4 x^{3} \cdot 3 + 6 x^{2} \cdot 3^{2} + 4 x \cdot 3^{3} + 3^{4} - 362 = 0$

Step 2.1.2

Simplify each term.

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Step 2.1.2.1

Multiply $3$ by $4$ .

$x^{4} + 12 x^{3} + 6 x^{2} \cdot 3^{2} + 4 x \cdot 3^{3} + 3^{4} - 362 = 0$

Step 2.1.2.2

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

$x^{4} + 12 x^{3} + 6 x^{2} \cdot 9 + 4 x \cdot 3^{3} + 3^{4} - 362 = 0$

Step 2.1.2.3

Multiply $9$ by $6$ .

$x^{4} + 12 x^{3} + 54 x^{2} + 4 x \cdot 3^{3} + 3^{4} - 362 = 0$

Step 2.1.2.4

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

$x^{4} + 12 x^{3} + 54 x^{2} + 4 x \cdot 27 + 3^{4} - 362 = 0$

Step 2.1.2.5

Multiply $27$ by $4$ .

$x^{4} + 12 x^{3} + 54 x^{2} + 108 x + 3^{4} - 362 = 0$

Step 2.1.2.6

Raise $3$ to the power of $4$ .

$x^{4} + 12 x^{3} + 54 x^{2} + 108 x + 81 - 362 = 0$

Step 2.2

Subtract $362$ from $81$ .

$x^{4} + 12 x^{3} + 54 x^{2} + 108 x - 281 = 0$

Step 3

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

$x \approx - 7.36191444, 1.36191444$

Step 4