Solve 6^2-14x^640

Question

Simplify the expression

36 - 560 x^{6}

Evaluate

6^{2} - 14 x^{6} \times 40

Multiply the terms

6^{2} - 560 x^{6}

Solution

36 - 560 x^{6}

Show Solution

4 (9 - 140 x^{6})

Evaluate

6^{2} - 14 x^{6} \times 40

Multiply the terms

6^{2} - 560 x^{6}

Solution

4 (9 - 140 x^{6})

Show Solution

x_{1} = - \frac{6 9 \times 14 0 ^{5}}{140}, x_{2} = \frac{6 9 \times 14 0 ^{5}}{140}

Alternative Form

x_{1} \approx - 0.632925, x_{2} \approx 0.632925

Evaluate

6^{2} - 14 x^{6} \times 40

To find the roots of the expression,set the expression equal to 0

6^{2} - 14 x^{6} \times 40 = 0

Multiply the terms

6^{2} - 560 x^{6} = 0

Evaluate the power

36 - 560 x^{6} = 0

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

- 560 x^{6} = 0 - 36

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

- 560 x^{6} = - 36

Change the signs on both sides of the equation

560 x^{6} = 36

Divide both sides

\frac{560 x ^{6}}{560} = \frac{36}{560}

Divide the numbers

x^{6} = \frac{36}{560}

Cancel out the common factor 4

x^{6} = \frac{9}{140}

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

x = \pm 6 \frac{9}{140}

Simplify the expression

More Steps

Evaluate

6 \frac{9}{140}

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

\frac{6 9}{6 140}

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}{6 140}

Multiply by the Conjugate

\frac{3 3 \times 6 14 0 ^{5}}{6 140 \times 6 14 0 ^{5}}

Multiply the numbers

More Steps

Evaluate

33 \times 6 14 0^{5}

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

6 3^{2} \times 6 14 0^{5}

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

6 3^{2} \times 14 0^{5}

Calculate the product

6 9 \times 14 0^{5}

\frac{6 9 \times 14 0 ^{5}}{6 140 \times 6 14 0 ^{5}}

Multiply the numbers

More Steps

Evaluate

6140 \times 6 14 0^{5}

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

6 140 \times 14 0^{5}

Calculate the product

6 14 0^{6}

Reduce the index of the radical and exponent with 6

140

\frac{6 9 \times 14 0 ^{5}}{140}

x = \pm \frac{6 9 \times 14 0 ^{5}}{140}

Separate the equation into 2 possible cases

x = \frac{6 9 \times 14 0 ^{5}}{140} x = - \frac{6 9 \times 14 0 ^{5}}{140}

Solution

x_{1} = - \frac{6 9 \times 14 0 ^{5}}{140}, x_{2} = \frac{6 9 \times 14 0 ^{5}}{140}

Alternative Form

x_{1} \approx - 0.632925, x_{2} \approx 0.632925

Show Solution