Solve x^4 4x^2-45x^4 4x^2 -45

Question

Simplify the expression

- 176 x^{6} - 45

Show Solution

x_{1} = - \frac{6 1215 \times 17 6 ^{5}}{352} - \frac{6 45 \times 17 6 ^{5}}{352} i, x_{2} = \frac{6 1215 \times 17 6 ^{5}}{352} + \frac{6 45 \times 17 6 ^{5}}{352} i

Alternative Form

x_{1} \approx - 0.689944 - 0.398339 i, x_{2} \approx 0.689944 + 0.398339 i

Evaluate

x^{4} \times 4 x^{2} - 45 x^{4} \times 4 x^{2} - 45

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

x^{4} \times 4 x^{2} - 45 x^{4} \times 4 x^{2} - 45 = 0

Multiply

More Steps

4 x^{6} - 45 x^{4} \times 4 x^{2} - 45 = 0

Multiply

More Steps

4 x^{6} - 180 x^{6} - 45 = 0

Subtract the terms

More Steps

- 176 x^{6} - 45 = 0

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

- 176 x^{6} = 0 + 45

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

- 176 x^{6} = 45

Change the signs on both sides of the equation

176 x^{6} = - 45

Divide both sides

\frac{176 x ^{6}}{176} = \frac{- 45}{176}

Divide the numbers

x^{6} = \frac{- 45}{176}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{6} = - \frac{45}{176}

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

x = \pm 6 - \frac{45}{176}

Simplify the expression

More Steps

x = \pm (\frac{6 1215 \times 17 6 ^{5}}{352} + \frac{6 45 \times 17 6 ^{5}}{352} i)

Separate the equation into 2 possible cases

x = \frac{6 1215 \times 17 6 ^{5}}{352} + \frac{6 45 \times 17 6 ^{5}}{352} i x = - \frac{6 1215 \times 17 6 ^{5}}{352} - \frac{6 45 \times 17 6 ^{5}}{352} i

Solution

x_{1} = - \frac{6 1215 \times 17 6 ^{5}}{352} - \frac{6 45 \times 17 6 ^{5}}{352} i, x_{2} = \frac{6 1215 \times 17 6 ^{5}}{352} + \frac{6 45 \times 17 6 ^{5}}{352} i

Alternative Form

x_{1} \approx - 0.689944 - 0.398339 i, x_{2} \approx 0.689944 + 0.398339 i

Show Solution