Solve (x^2-8)^2 4(x^2-8)-5=0

Question

Solve the equation

x_{1} = - \frac{2 3 10 + 32}{2}, x_{2} = \frac{2 3 10 + 32}{2}

Alternative Form

x_{1} \approx - 3.012842, x_{2} \approx 3.012842

Evaluate

(x^{2} - 8)^{2} \times 4 (x^{2} - 8) - 5 = 0

Multiply

More Steps

4 (x^{2} - 8)^{3} - 5 = 0

Add or subtract both sides

4 (x^{2} - 8)^{3} = 0 + 5

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

4 (x^{2} - 8)^{3} = 5

Divide both sides

\frac{4 ( x ^{2} - 8 ) ^{3}}{4} = \frac{5}{4}

Divide the numbers

(x^{2} - 8)^{3} = \frac{5}{4}

Take the 3 -th root on both sides of the equation

3 (x^{2} - 8)^{3} = 3 \frac{5}{4}

Calculate

x^{2} - 8 = 3 \frac{5}{4}

Simplify the root

More Steps

x^{2} - 8 = \frac{3 10}{2}

Add or subtract both sides

x^{2} = \frac{3 10 + 16}{2}

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

x = \pm \frac{3 10 + 16}{2}

Simplify the expression

x = \pm \frac{2 3 10 + 32}{2}

Separate the equation into 2 possible cases

x = \frac{2 3 10 + 32}{2} x = - \frac{2 3 10 + 32}{2}

Solution

x_{1} = - \frac{2 3 10 + 32}{2}, x_{2} = \frac{2 3 10 + 32}{2}

Alternative Form

x_{1} \approx - 3.012842, x_{2} \approx 3.012842

Show Solution