Solve x^4-113x^2+3136=0

$$x ^ { 4 } - 113 x ^ { 2 } + 3136 = 0$$

Solve for x

$$x=-8$$

$$x=8$$

$$x=7$$

$$x=-7$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-113t+3136=0$$

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, -113 for b, and 3136 for c in the quadratic formula.

$$t=\frac{-\left(-113\right)±\sqrt{\left(-113\right)^{2}-4\times 1\times 3136}}{2}$$

Do the calculations.

$$t=\frac{113±15}{2}$$

Solve the equation t=\frac{113±15}{2} when ± is plus and when ± is minus.

$$t=64 t=49$$

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

$$x=8 x=-8 x=7 x=-7$$