Solve x^2=(12-0.2x)div2

$${ x }^{ 2 } = (12-0.2x) \div 2$$

Solve for x

$$x=-2.5$$

$$x=2.4$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$2x^{2}=12-0.2x$$

Subtract 12 from both sides.

$$2x^{2}-12=-0.2x$$

Add 0.2x to both sides.

$$2x^{2}-12+0.2x=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$2x^{2}+0.2x-12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0.2 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-0.2±\sqrt{0.2^{2}-4\times 2\left(-12\right)}}{2\times 2}$$

Square 0.2 by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-0.2±\sqrt{0.04-4\times 2\left(-12\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-0.2±\sqrt{0.04-8\left(-12\right)}}{2\times 2}$$

Multiply -8 times -12.

$$x=\frac{-0.2±\sqrt{0.04+96}}{2\times 2}$$

Add 0.04 to 96.

$$x=\frac{-0.2±\sqrt{96.04}}{2\times 2}$$

Take the square root of 96.04.

$$x=\frac{-0.2±\frac{49}{5}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-0.2±\frac{49}{5}}{4}$$

Now solve the equation x=\frac{-0.2±\frac{49}{5}}{4} when ± is plus. Add -0.2 to \frac{49}{5} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{\frac{48}{5}}{4}$$

Divide \frac{48}{5} by 4.

$$x=\frac{12}{5}$$

Now solve the equation x=\frac{-0.2±\frac{49}{5}}{4} when ± is minus. Subtract \frac{49}{5} from -0.2 by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{10}{4}$$

Reduce the fraction \frac{-10}{4} to lowest terms by extracting and canceling out 2.

$$x=-\frac{5}{2}$$

The equation is now solved.

$$x=\frac{12}{5} x=-\frac{5}{2}$$

Steps for Completing the Square

Multiply both sides of the equation by 2.

$$2x^{2}=12-0.2x$$

Add 0.2x to both sides.

$$2x^{2}+0.2x=12$$

Divide both sides by 2.

$$\frac{2x^{2}+0.2x}{2}=\frac{12}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\frac{0.2}{2}x=\frac{12}{2}$$

Divide 0.2 by 2.

$$x^{2}+0.1x=\frac{12}{2}$$

Divide 12 by 2.

$$x^{2}+0.1x=6$$

Divide 0.1, the coefficient of the x term, by 2 to get 0.05. Then add the square of 0.05 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+0.1x+0.05^{2}=6+0.05^{2}$$

Square 0.05 by squaring both the numerator and the denominator of the fraction.

$$x^{2}+0.1x+0.0025=6+0.0025$$

Add 6 to 0.0025.

$$x^{2}+0.1x+0.0025=6.0025$$

Factor x^{2}+0.1x+0.0025. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+0.05\right)^{2}=6.0025$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+0.05\right)^{2}}=\sqrt{6.0025}$$

Simplify.

$$x+0.05=\frac{49}{20} x+0.05=-\frac{49}{20}$$

Subtract 0.05 from both sides of the equation.

$$x=\frac{12}{5} x=-\frac{5}{2}$$