Solve x^3+6x^2-15=x^3+1

$${ x }^{ 3 } +6 { x }^{ 2 } -15= { x }^{ 3 } +1$$

Solve for x

$$x = \frac{2 \sqrt{6}}{3} \approx 1.632993162$$

$$x = -\frac{2 \sqrt{6}}{3} \approx -1.632993162$$

Steps by Finding Square Root

Subtract x^{3} from both sides.

$$x^{3}+6x^{2}-15-x^{3}=1$$

Combine x^{3} and -x^{3} to get 0.

$$6x^{2}-15=1$$

Add 15 to both sides.

$$6x^{2}=1+15$$

Add 1 and 15 to get 16.

$$6x^{2}=16$$

Divide both sides by 6.

$$x^{2}=\frac{16}{6}$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{8}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{6}}{3} x=-\frac{2\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

Subtract x^{3} from both sides.

$$x^{3}+6x^{2}-15-x^{3}=1$$

Combine x^{3} and -x^{3} to get 0.

$$6x^{2}-15=1$$

Subtract 1 from both sides.

$$6x^{2}-15-1=0$$

Subtract 1 from -15 to get -16.

$$6x^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-16\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-16\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-16\right)}}{2\times 6}$$

Multiply -24 times -16.

$$x=\frac{0±\sqrt{384}}{2\times 6}$$

Take the square root of 384.

$$x=\frac{0±8\sqrt{6}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±8\sqrt{6}}{12}$$

Now solve the equation x=\frac{0±8\sqrt{6}}{12} when ± is plus.

$$x=\frac{2\sqrt{6}}{3}$$

Now solve the equation x=\frac{0±8\sqrt{6}}{12} when ± is minus.

$$x=-\frac{2\sqrt{6}}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{6}}{3} x=-\frac{2\sqrt{6}}{3}$$