Solve x^4-23x^2+112=0

$${ x }^{ 4 } -23 { x }^{ 2 } +112=0$$

Solve for x

$$x=-4$$

$$x=4$$

$$x=\sqrt{7}\approx 2.645751311$$

$$x=-\sqrt{7}\approx -2.645751311$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-23t+112=0$$

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, -23 for b, and 112 for c in the quadratic formula.

$$t=\frac{-\left(-23\right)±\sqrt{\left(-23\right)^{2}-4\times 1\times 112}}{2}$$

Do the calculations.

$$t=\frac{23±9}{2}$$

Solve the equation t=\frac{23±9}{2} when ± is plus and when ± is minus.

$$t=16 t=7$$

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

$$x=4 x=-4 x=\sqrt{7} x=-\sqrt{7}$$