Solve 0.5x^2=x+4

$$0.5 { x }^{ 2 } =x+4$$

Solve for x

$$x=-2$$

$$x=4$$

Steps Using the Quadratic Formula

Subtract x from both sides.

$$0.5x^{2}-x=4$$

Subtract 4 from both sides.

$$0.5x^{2}-x-4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.5 for a, -1 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 0.5\left(-4\right)}}{2\times 0.5}$$

Multiply -4 times 0.5.

$$x=\frac{-\left(-1\right)±\sqrt{1-2\left(-4\right)}}{2\times 0.5}$$

Multiply -2 times -4.

$$x=\frac{-\left(-1\right)±\sqrt{1+8}}{2\times 0.5}$$

Add 1 to 8.

$$x=\frac{-\left(-1\right)±\sqrt{9}}{2\times 0.5}$$

Take the square root of 9.

$$x=\frac{-\left(-1\right)±3}{2\times 0.5}$$

The opposite of -1 is 1.

$$x=\frac{1±3}{2\times 0.5}$$

Multiply 2 times 0.5.

$$x=\frac{1±3}{1}$$

Now solve the equation x=\frac{1±3}{1} when ± is plus. Add 1 to 3.

$$x=\frac{4}{1}$$

Divide 4 by 1.

$$x=4$$

Now solve the equation x=\frac{1±3}{1} when ± is minus. Subtract 3 from 1.

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

Divide -2 by 1.

$$x=-2$$

The equation is now solved.

$$x=4 x=-2$$

Steps for Completing the Square

Subtract x from both sides.

$$0.5x^{2}-x=4$$

Multiply both sides by 2.

$$\frac{0.5x^{2}-x}{0.5}=\frac{4}{0.5}$$

Dividing by 0.5 undoes the multiplication by 0.5.

$$x^{2}+\left(-\frac{1}{0.5}\right)x=\frac{4}{0.5}$$

Divide -1 by 0.5 by multiplying -1 by the reciprocal of 0.5.

$$x^{2}-2x=\frac{4}{0.5}$$

Divide 4 by 0.5 by multiplying 4 by the reciprocal of 0.5.

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

Divide -2, the coefficient of the x term, by 2 to get -1. Then add the square of -1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-2x+1=8+1$$

Add 8 to 1.

$$x^{2}-2x+1=9$$

Factor x^{2}-2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-1\right)^{2}=9$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{9}$$

Simplify.

$$x-1=3 x-1=-3$$

Add 1 to both sides of the equation.

$$x=4 x=-2$$