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

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

Solve for x

$$x=\frac{3-\sqrt{17}}{2}\approx -0.561552813$$

$$x=\frac{\sqrt{17}-3}{2}\approx 0.561552813$$

$$x = \frac{\sqrt{17} + 3}{2} \approx 3.561552813$$

$$x=\frac{-\sqrt{17}-3}{2}\approx -3.561552813$$

Steps Using the Quadratic Formula

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

Substitute t for x^{2}.

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

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, -13 for b, and 4 for c in the quadratic formula.

$$t=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\times 1\times 4}}{2}$$

Do the calculations.

$$t=\frac{13±3\sqrt{17}}{2}$$

Solve the equation t=\frac{13±3\sqrt{17}}{2} when ± is plus and when ± is minus.

$$t=\frac{3\sqrt{17}+13}{2} t=\frac{13-3\sqrt{17}}{2}$$

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

$$x=\frac{\sqrt{17}+3}{2} x=-\frac{\sqrt{17}+3}{2} x=-\frac{3-\sqrt{17}}{2} x=\frac{3-\sqrt{17}}{2}$$