Solve x^4-89x^2=-1600

$$x ^ { 4 } - 89 x ^ { 2 } = - 1600$$

Solve for x

$$x=-8$$

$$x=8$$

$$x=5$$

$$x=-5$$

Steps Using the Quadratic Formula

Add 1600 to both sides.

$$x^{4}-89x^{2}+1600=0$$

Substitute t for x^{2}.

$$t^{2}-89t+1600=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, -89 for b, and 1600 for c in the quadratic formula.

$$t=\frac{-\left(-89\right)±\sqrt{\left(-89\right)^{2}-4\times 1\times 1600}}{2}$$

Do the calculations.

$$t=\frac{89±39}{2}$$

Solve the equation t=\frac{89±39}{2} when ± is plus and when ± is minus.

$$t=64 t=25$$

Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for each t.

$$x=8 x=-8 x=5 x=-5$$