Solve 4y^4+7y^2-36=0

$$4 y ^ { 4 } + 7 y ^ { 2 } - 36 = 0$$

Solve for y (complex solution)

$$y = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$y = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

$$y=-2i$$

$$y=2i$$

Steps Using the Quadratic Formula

Substitute t for y^{2}.

$$4t^{2}+7t-36=0$$

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 4 for a, 7 for b, and -36 for c in the quadratic formula.

$$t=\frac{-7±\sqrt{7^{2}-4\times 4\left(-36\right)}}{2\times 4}$$

Do the calculations.

$$t=\frac{-7±25}{8}$$

Solve the equation t=\frac{-7±25}{8} when ± is plus and when ± is minus.

$$t=\frac{9}{4} t=-4$$

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

$$y=-\frac{3}{2} y=\frac{3}{2} y=-2i y=2i$$

Solve for y

$$y = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

$$y = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps Using the Quadratic Formula

Substitute t for y^{2}.

$$4t^{2}+7t-36=0$$

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 4 for a, 7 for b, and -36 for c in the quadratic formula.

$$t=\frac{-7±\sqrt{7^{2}-4\times 4\left(-36\right)}}{2\times 4}$$

Do the calculations.

$$t=\frac{-7±25}{8}$$

Solve the equation t=\frac{-7±25}{8} when ± is plus and when ± is minus.

$$t=\frac{9}{4} t=-4$$

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

$$y=\frac{3}{2} y=-\frac{3}{2}$$