Solve 4x^4-13x^2+9=0

$$4 { x }^{ 4 } -13 { x }^{ 2 } +9=0$$

Solve for x

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

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

$$x=1$$

$$x=-1$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$4t^{2}-13t+9=0$$

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, -13 for b, and 9 for c in the quadratic formula.

$$t=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\times 4\times 9}}{2\times 4}$$

Do the calculations.

$$t=\frac{13±5}{8}$$

Solve the equation t=\frac{13±5}{8} when ± is plus and when ± is minus.

$$t=\frac{9}{4} t=1$$

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

$$x=\frac{3}{2} x=-\frac{3}{2} x=1 x=-1$$