Solve s^4-11s^2+28=0

$$s ^ { 4 } - 11 s ^ { 2 } + 28 = 0$$

Solve for s

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

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

$$s=2$$

$$s=-2$$

Steps Using the Quadratic Formula

Substitute t for s^{2}.

$$t^{2}-11t+28=0$$

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, -11 for b, and 28 for c in the quadratic formula.

$$t=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\times 1\times 28}}{2}$$

Do the calculations.

$$t=\frac{11±3}{2}$$

Solve the equation t=\frac{11±3}{2} when ± is plus and when ± is minus.

$$t=7 t=4$$

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

$$s=\sqrt{7} s=-\sqrt{7} s=2 s=-2$$