Solve 7x^4-6=19 - ScanMath

Question

Solve the equation

x_{1} = - \frac{4 8575}{7}, x_{2} = \frac{4 8575}{7}

Alternative Form

x_{1} \approx - 1.374708, x_{2} \approx 1.374708

Evaluate

7 x^{4} - 6 = 19

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

7 x^{4} = 19 + 6

Add the numbers

7 x^{4} = 25

Divide both sides

\frac{7 x ^{4}}{7} = \frac{25}{7}

Divide the numbers

x^{4} = \frac{25}{7}

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

x = \pm 4 \frac{25}{7}

Simplify the expression

More Steps

Evaluate

4 \frac{25}{7}

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

\frac{4 25}{4 7}

Simplify the radical expression

More Steps

Evaluate

425

Write the number in exponential form with the base of 5

4 5^{2}

Reduce the index of the radical and exponent with 2

5

\frac{5}{4 7}

Multiply by the Conjugate

\frac{5 \times 4 7 ^{3}}{4 7 \times 4 7 ^{3}}

Simplify

\frac{5 \times 4 343}{4 7 \times 4 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

5 \times 4343

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

4 5^{2} \times 4343

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

4 5^{2} \times 343

Calculate the product

48575

\frac{4 8575}{4 7 \times 4 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

47 \times 4 7^{3}

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

4 7 \times 7^{3}

Calculate the product

4 7^{4}

Reduce the index of the radical and exponent with 4

7

\frac{4 8575}{7}

x = \pm \frac{4 8575}{7}

Separate the equation into 2 possible cases

x = \frac{4 8575}{7} x = - \frac{4 8575}{7}

Solution

x_{1} = - \frac{4 8575}{7}, x_{2} = \frac{4 8575}{7}

Alternative Form

x_{1} \approx - 1.374708, x_{2} \approx 1.374708

Show Solution