Solve 32x^10-63x^5-2=0

$$32 x ^ { 10 } - 63 x ^ { 5 } - 2 = 0$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

$$x=\sqrt[5]{2}\approx 1.148698355$$

Steps Using the Quadratic Formula

Substitute t for x^{5}.

$$32t^{2}-63t-2=0$$

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 32 for a, -63 for b, and -2 for c in the quadratic formula.

$$t=\frac{-\left(-63\right)±\sqrt{\left(-63\right)^{2}-4\times 32\left(-2\right)}}{2\times 32}$$

Do the calculations.

$$t=\frac{63±65}{64}$$

Solve the equation t=\frac{63±65}{64} when ± is plus and when ± is minus.

$$t=2 t=-\frac{1}{32}$$

Since x=t^{5}, the solutions are obtained by evaluating x=\sqrt[5]{t} for each t.

$$x=\sqrt[5]{2} x=-\frac{1}{2}$$