Solve 4=x^2+2x*8

$$4 = x ^ { 2 } + 2 x \cdot 8$$

Solve for x

$$x=2\sqrt{17}-8\approx 0.246211251$$

$$x=-2\sqrt{17}-8\approx -16.246211251$$

Steps Using the Quadratic Formula

Multiply 2 and 8 to get 16.

$$4=x^{2}+16x$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+16x=4$$

Subtract 4 from both sides.

$$x^{2}+16x-4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 16 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 16.

$$x=\frac{-16±\sqrt{256-4\left(-4\right)}}{2}$$

Multiply -4 times -4.

$$x=\frac{-16±\sqrt{256+16}}{2}$$

Add 256 to 16.

$$x=\frac{-16±\sqrt{272}}{2}$$

Take the square root of 272.

$$x=\frac{-16±4\sqrt{17}}{2}$$

Now solve the equation x=\frac{-16±4\sqrt{17}}{2} when ± is plus. Add -16 to 4\sqrt{17}.

$$x=\frac{4\sqrt{17}-16}{2}$$

Divide -16+4\sqrt{17} by 2.

$$x=2\sqrt{17}-8$$

Now solve the equation x=\frac{-16±4\sqrt{17}}{2} when ± is minus. Subtract 4\sqrt{17} from -16.

$$x=\frac{-4\sqrt{17}-16}{2}$$

Divide -16-4\sqrt{17} by 2.

$$x=-2\sqrt{17}-8$$

The equation is now solved.

$$x=2\sqrt{17}-8 x=-2\sqrt{17}-8$$

Steps for Completing the Square

Multiply 2 and 8 to get 16.

$$4=x^{2}+16x$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+16x=4$$

Divide 16, the coefficient of the x term, by 2 to get 8. Then add the square of 8 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+16x+8^{2}=4+8^{2}$$

Square 8.

$$x^{2}+16x+64=4+64$$

Add 4 to 64.

$$x^{2}+16x+64=68$$

Factor x^{2}+16x+64. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+8\right)^{2}=68$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+8\right)^{2}}=\sqrt{68}$$

Simplify.

$$x+8=2\sqrt{17} x+8=-2\sqrt{17}$$

Subtract 8 from both sides of the equation.

$$x=2\sqrt{17}-8 x=-2\sqrt{17}-8$$