Solve v^6+7v^3=8

$$v ^ { 6 } + 7 v ^ { 3 } = 8$$

Solve for v

$$v=-2$$

$$v=1$$

Steps Using the Quadratic Formula

Subtract 8 from both sides.

$$v^{6}+7v^{3}-8=0$$

Substitute t for v^{3}.

$$t^{2}+7t-8=0$$

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, 7 for b, and -8 for c in the quadratic formula.

$$t=\frac{-7±\sqrt{7^{2}-4\times 1\left(-8\right)}}{2}$$

Do the calculations.

$$t=\frac{-7±9}{2}$$

Solve the equation t=\frac{-7±9}{2} when ± is plus and when ± is minus.

$$t=1 t=-8$$

Since v=t^{3}, the solutions are obtained by evaluating v=\sqrt[3]{t} for each t.

$$v=1 v=-2$$