Solve 16*x^4-136x^2+225=0

$$16 \times { x }^{ 4 } -136 { x }^{ 2 } +225 = 0$$

Solve for x

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

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

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

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$16t^{2}-136t+225=0$$

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 16 for a, -136 for b, and 225 for c in the quadratic formula.

$$t=\frac{-\left(-136\right)±\sqrt{\left(-136\right)^{2}-4\times 16\times 225}}{2\times 16}$$

Do the calculations.

$$t=\frac{136±64}{32}$$

Solve the equation t=\frac{136±64}{32} when ± is plus and when ± is minus.

$$t=\frac{25}{4} t=\frac{9}{4}$$

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

$$x=\frac{5}{2} x=-\frac{5}{2} x=\frac{3}{2} x=-\frac{3}{2}$$