Solve y^4+3600=169y^2

$${ y }^{ 4 } +3600 = 169 { y }^{ 2 }$$

Solve for y

$$y=-12$$

$$y=12$$

$$y=5$$

$$y=-5$$

Steps Using the Quadratic Formula

Subtract 169y^{2} from both sides.

$$y^{4}+3600-169y^{2}=0$$

Substitute t for y^{2}.

$$t^{2}-169t+3600=0$$

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, -169 for b, and 3600 for c in the quadratic formula.

$$t=\frac{-\left(-169\right)±\sqrt{\left(-169\right)^{2}-4\times 1\times 3600}}{2}$$

Do the calculations.

$$t=\frac{169±119}{2}$$

Solve the equation t=\frac{169±119}{2} when ± is plus and when ± is minus.

$$t=144 t=25$$

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

$$y=12 y=-12 y=5 y=-5$$