Solve 2x^33x 12=90

Question

Solve the equation

x_{1} = - \frac{4 20}{2}, x_{2} = \frac{4 20}{2}

Alternative Form

x_{1} \approx - 1.057371, x_{2} \approx 1.057371

Evaluate

2 x^{3} \times 3 x \times 12 = 90

Multiply

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Evaluate

2 x^{3} \times 3 x \times 12

Multiply the terms

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Evaluate

2 \times 3 \times 12

Multiply the terms

6 \times 12

Multiply the numbers

72

72 x^{3} \times x

Multiply the terms with the same base by adding their exponents

72 x^{3 + 1}

Add the numbers

72 x^{4}

72 x^{4} = 90

Divide both sides

\frac{72 x ^{4}}{72} = \frac{90}{72}

Divide the numbers

x^{4} = \frac{90}{72}

Cancel out the common factor 18

x^{4} = \frac{5}{4}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 \frac{5}{4}

Simplify the expression

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Evaluate

4 \frac{5}{4}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4 5}{4 4}

Simplify the radical expression

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Evaluate

44

Write the number in exponential form with the base of 2

4 2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{4 5}{2}

Multiply by the Conjugate

\frac{4 5 \times 2}{2 \times 2}

Multiply the numbers

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Evaluate

45 \times 2

Use n a = mn a^{m} to expand the expression

45 \times 4 2^{2}

The product of roots with the same index is equal to the root of the product

4 5 \times 2^{2}

Calculate the product

420

\frac{4 20}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{4 20}{2}

x = \pm \frac{4 20}{2}

Separate the equation into 2 possible cases

x = \frac{4 20}{2} x = - \frac{4 20}{2}

Solution

x_{1} = - \frac{4 20}{2}, x_{2} = \frac{4 20}{2}

Alternative Form

x_{1} \approx - 1.057371, x_{2} \approx 1.057371

Show Solution