Solve 4x^(4) 142x^(2)-72=0

Question

Solve the equation

x_{1} = - \frac{6 9 \times 7 1 ^{5}}{71}, x_{2} = \frac{6 9 \times 7 1 ^{5}}{71}

Alternative Form

x_{1} \approx - 0.708757, x_{2} \approx 0.708757

Evaluate

4 x^{4} \times 142 x^{2} - 72 = 0

Multiply

More Steps

Evaluate

4 x^{4} \times 142 x^{2}

Multiply the terms

568 x^{4} \times x^{2}

Multiply the terms with the same base by adding their exponents

568 x^{4 + 2}

Add the numbers

568 x^{6}

568 x^{6} - 72 = 0

Move the constant to the right-hand side and change its sign

568 x^{6} = 0 + 72

Removing 0 doesn't change the value,so remove it from the expression

568 x^{6} = 72

Divide both sides

\frac{568 x ^{6}}{568} = \frac{72}{568}

Divide the numbers

x^{6} = \frac{72}{568}

Cancel out the common factor 8

x^{6} = \frac{9}{71}

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

x = \pm 6 \frac{9}{71}

Simplify the expression

More Steps

Evaluate

6 \frac{9}{71}

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

\frac{6 9}{6 71}

Simplify the radical expression

More Steps

Evaluate

69

Write the number in exponential form with the base of 3

6 3^{2}

Reduce the index of the radical and exponent with 2

33

\frac{3 3}{6 71}

Multiply by the Conjugate

\frac{3 3 \times 6 7 1 ^{5}}{6 71 \times 6 7 1 ^{5}}

Multiply the numbers

More Steps

Evaluate

33 \times 6 7 1^{5}

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

6 3^{2} \times 6 7 1^{5}

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

6 3^{2} \times 7 1^{5}

Calculate the product

6 9 \times 7 1^{5}

\frac{6 9 \times 7 1 ^{5}}{6 71 \times 6 7 1 ^{5}}

Multiply the numbers

More Steps

Evaluate

671 \times 6 7 1^{5}

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

6 71 \times 7 1^{5}

Calculate the product

6 7 1^{6}

Reduce the index of the radical and exponent with 6

71

\frac{6 9 \times 7 1 ^{5}}{71}

x = \pm \frac{6 9 \times 7 1 ^{5}}{71}

Separate the equation into 2 possible cases

x = \frac{6 9 \times 7 1 ^{5}}{71} x = - \frac{6 9 \times 7 1 ^{5}}{71}

Solution

x_{1} = - \frac{6 9 \times 7 1 ^{5}}{71}, x_{2} = \frac{6 9 \times 7 1 ^{5}}{71}

Alternative Form

x_{1} \approx - 0.708757, x_{2} \approx 0.708757

Show Solution