Solve y^4+7y^2-44=0

$$y ^ { 4 } + 7 y ^ { 2 } - 44 = 0$$

Solve for y (complex solution)

$$y=2$$

$$y=-2$$

$$y=-\sqrt{11}i\approx -0-3.31662479i$$

$$y=\sqrt{11}i\approx 3.31662479i$$

Steps Using the Quadratic Formula

Substitute t for y^{2}.

$$t^{2}+7t-44=0$$

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, 7 for b, and -44 for c in the quadratic formula.

$$t=\frac{-7±\sqrt{7^{2}-4\times 1\left(-44\right)}}{2}$$

Do the calculations.

$$t=\frac{-7±15}{2}$$

Solve the equation t=\frac{-7±15}{2} when ± is plus and when ± is minus.

$$t=4 t=-11$$

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

$$y=-2 y=2 y=-\sqrt{11}i y=\sqrt{11}i$$

Solve for y

$$y=-2$$

$$y=2$$

Steps Using the Quadratic Formula

Substitute t for y^{2}.

$$t^{2}+7t-44=0$$

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, 7 for b, and -44 for c in the quadratic formula.

$$t=\frac{-7±\sqrt{7^{2}-4\times 1\left(-44\right)}}{2}$$

Do the calculations.

$$t=\frac{-7±15}{2}$$

Solve the equation t=\frac{-7±15}{2} when ± is plus and when ± is minus.

$$t=4 t=-11$$

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

$$y=2 y=-2$$