Solve 3x^453x^45=180 - Socratic AI (ScanMath)

Question

Solve the equation

x_{1} = - \frac{8 12 \times 5 3 ^{7}}{53}, x_{2} = \frac{8 12 \times 5 3 ^{7}}{53}

Alternative Form

x_{1} \approx - 0.830545, x_{2} \approx 0.830545

Evaluate

3 x^{4} \times 53 x^{4} \times 5 = 180

Multiply

More Steps

Evaluate

3 x^{4} \times 53 x^{4} \times 5

Multiply the terms

More Steps

Evaluate

3 \times 53 \times 5

Multiply the terms

159 \times 5

Multiply the numbers

795

795 x^{4} \times x^{4}

Multiply the terms with the same base by adding their exponents

795 x^{4 + 4}

Add the numbers

795 x^{8}

795 x^{8} = 180

Divide both sides

\frac{795 x ^{8}}{795} = \frac{180}{795}

Divide the numbers

x^{8} = \frac{180}{795}

Cancel out the common factor 15

x^{8} = \frac{12}{53}

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

x = \pm 8 \frac{12}{53}

Simplify the expression

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Evaluate

8 \frac{12}{53}

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

\frac{8 12}{8 53}

Multiply by the Conjugate

\frac{8 12 \times 8 5 3 ^{7}}{8 53 \times 8 5 3 ^{7}}

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

\frac{8 12 \times 5 3 ^{7}}{8 53 \times 8 5 3 ^{7}}

Multiply the numbers

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Evaluate

853 \times 8 5 3^{7}

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

8 53 \times 5 3^{7}

Calculate the product

8 5 3^{8}

Reduce the index of the radical and exponent with 8

53

\frac{8 12 \times 5 3 ^{7}}{53}

x = \pm \frac{8 12 \times 5 3 ^{7}}{53}

Separate the equation into 2 possible cases

x = \frac{8 12 \times 5 3 ^{7}}{53} x = - \frac{8 12 \times 5 3 ^{7}}{53}

Solution

x_{1} = - \frac{8 12 \times 5 3 ^{7}}{53}, x_{2} = \frac{8 12 \times 5 3 ^{7}}{53}

Alternative Form

x_{1} \approx - 0.830545, x_{2} \approx 0.830545

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