Solve j^2-7j^6 - ScanMath

Question

Factor the expression

j^{2} (1 - 7 j^{4})

Evaluate

j^{2} - 7 j^{6}

Rewrite the expression

j^{2} - j^{2} \times 7 j^{4}

Solution

j^{2} (1 - 7 j^{4})

Show Solution

j_{1} = - \frac{4 343}{7}, j_{2} = 0, j_{3} = \frac{4 343}{7}

Alternative Form

j_{1} \approx - 0.614788, j_{2} = 0, j_{3} \approx 0.614788

Evaluate

j^{2} - 7 j^{6}

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

j^{2} - 7 j^{6} = 0

Factor the expression

j^{2} (1 - 7 j^{4}) = 0

Separate the equation into 2 possible cases

j^{2} = 0 1 - 7 j^{4} = 0

The only way a power can be 0 is when the base equals 0

j = 0 1 - 7 j^{4} = 0

Solve the equation

More Steps

Evaluate

1 - 7 j^{4} = 0

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

- 7 j^{4} = 0 - 1

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

- 7 j^{4} = - 1

Change the signs on both sides of the equation

7 j^{4} = 1

Divide both sides

\frac{7 j ^{4}}{7} = \frac{1}{7}

Divide the numbers

j^{4} = \frac{1}{7}

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

j = \pm 4 \frac{1}{7}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{7}

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

\frac{4 1}{4 7}

Simplify the radical expression

\frac{1}{4 7}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

\frac{4 343}{7}

j = \pm \frac{4 343}{7}

Separate the equation into 2 possible cases

j = \frac{4 343}{7} j = - \frac{4 343}{7}

j = 0 j = \frac{4 343}{7} j = - \frac{4 343}{7}

Solution

j_{1} = - \frac{4 343}{7}, j_{2} = 0, j_{3} = \frac{4 343}{7}

Alternative Form

j_{1} \approx - 0.614788, j_{2} = 0, j_{3} \approx 0.614788

Show Solution