Solve x^2=-8x+3

$$x ^ { 2 } = - 8 x + 3$$

Solve for x (complex solution)

$$x=\sqrt{19}-4\approx 0.358898944$$

$$x=-\left(\sqrt{19}+4\right)\approx -8.358898944$$

Steps Using the Quadratic Formula

Add 8x to both sides.

$$x^{2}+8x=3$$

Subtract 3 from both sides.

$$x^{2}+8x-3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 8 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-3\right)}}{2}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\left(-3\right)}}{2}$$

Multiply -4 times -3.

$$x=\frac{-8±\sqrt{64+12}}{2}$$

Add 64 to 12.

$$x=\frac{-8±\sqrt{76}}{2}$$

Take the square root of 76.

$$x=\frac{-8±2\sqrt{19}}{2}$$

Now solve the equation x=\frac{-8±2\sqrt{19}}{2} when ± is plus. Add -8 to 2\sqrt{19}.

$$x=\frac{2\sqrt{19}-8}{2}$$

Divide -8+2\sqrt{19} by 2.

$$x=\sqrt{19}-4$$

Now solve the equation x=\frac{-8±2\sqrt{19}}{2} when ± is minus. Subtract 2\sqrt{19} from -8.

$$x=\frac{-2\sqrt{19}-8}{2}$$

Divide -8-2\sqrt{19} by 2.

$$x=-\sqrt{19}-4$$

The equation is now solved.

$$x=\sqrt{19}-4 x=-\sqrt{19}-4$$

Steps for Completing the Square

Add 8x to both sides.

$$x^{2}+8x=3$$

Divide 8, the coefficient of the x term, by 2 to get 4. Then add the square of 4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+8x+4^{2}=3+4^{2}$$

Square 4.

$$x^{2}+8x+16=3+16$$

Add 3 to 16.

$$x^{2}+8x+16=19$$

Factor x^{2}+8x+16. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+4\right)^{2}=19$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{19}$$

Simplify.

$$x+4=\sqrt{19} x+4=-\sqrt{19}$$

Subtract 4 from both sides of the equation.

$$x=\sqrt{19}-4 x=-\sqrt{19}-4$$

Solve for x

$$x=\sqrt{19}-4\approx 0.358898944$$

$$x=-\sqrt{19}-4\approx -8.358898944$$

Steps Using the Quadratic Formula

Add 8x to both sides.

$$x^{2}+8x=3$$

Subtract 3 from both sides.

$$x^{2}+8x-3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 8 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-3\right)}}{2}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\left(-3\right)}}{2}$$

Multiply -4 times -3.

$$x=\frac{-8±\sqrt{64+12}}{2}$$

Add 64 to 12.

$$x=\frac{-8±\sqrt{76}}{2}$$

Take the square root of 76.

$$x=\frac{-8±2\sqrt{19}}{2}$$

Now solve the equation x=\frac{-8±2\sqrt{19}}{2} when ± is plus. Add -8 to 2\sqrt{19}.

$$x=\frac{2\sqrt{19}-8}{2}$$

Divide -8+2\sqrt{19} by 2.

$$x=\sqrt{19}-4$$

Now solve the equation x=\frac{-8±2\sqrt{19}}{2} when ± is minus. Subtract 2\sqrt{19} from -8.

$$x=\frac{-2\sqrt{19}-8}{2}$$

Divide -8-2\sqrt{19} by 2.

$$x=-\sqrt{19}-4$$

The equation is now solved.

$$x=\sqrt{19}-4 x=-\sqrt{19}-4$$

Steps for Completing the Square

Add 8x to both sides.

$$x^{2}+8x=3$$

Divide 8, the coefficient of the x term, by 2 to get 4. Then add the square of 4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+8x+4^{2}=3+4^{2}$$

Square 4.

$$x^{2}+8x+16=3+16$$

Add 3 to 16.

$$x^{2}+8x+16=19$$

Factor x^{2}+8x+16. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+4\right)^{2}=19$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{19}$$

Simplify.

$$x+4=\sqrt{19} x+4=-\sqrt{19}$$

Subtract 4 from both sides of the equation.

$$x=\sqrt{19}-4 x=-\sqrt{19}-4$$