Solve 135x^4+72x^2-144=0

$$135 x ^ { 4 } + 72 x ^ { 2 } - 144 = 0$$

Solve for x (complex solution)

$$x=\frac{2\sqrt{5}}{5}\approx 0.894427191$$

$$x=-\frac{2\sqrt{5}}{5}\approx -0.894427191$$

$$x=-\frac{2\sqrt{3}i}{3}\approx -0-1.154700538i$$

$$x=\frac{2\sqrt{3}i}{3}\approx 1.154700538i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$135t^{2}+72t-144=0$$

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 135 for a, 72 for b, and -144 for c in the quadratic formula.

$$t=\frac{-72±\sqrt{72^{2}-4\times 135\left(-144\right)}}{2\times 135}$$

Do the calculations.

$$t=\frac{-72±288}{270}$$

Solve the equation t=\frac{-72±288}{270} when ± is plus and when ± is minus.

$$t=\frac{4}{5} t=-\frac{4}{3}$$

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

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

Solve for x

$$x=-\frac{2\sqrt{5}}{5}\approx -0.894427191$$

$$x=\frac{2\sqrt{5}}{5}\approx 0.894427191$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$135t^{2}+72t-144=0$$

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 135 for a, 72 for b, and -144 for c in the quadratic formula.

$$t=\frac{-72±\sqrt{72^{2}-4\times 135\left(-144\right)}}{2\times 135}$$

Do the calculations.

$$t=\frac{-72±288}{270}$$

Solve the equation t=\frac{-72±288}{270} when ± is plus and when ± is minus.

$$t=\frac{4}{5} t=-\frac{4}{3}$$

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

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