Solve x^2=1.13*1.13-1.13x

$$x ^ { 2 } = 1.13 \times 1.13 - 1.13 x$$

Solve for x

$$x=\frac{113\sqrt{5}-113}{200}\approx 0.698378407$$

$$x=\frac{-113\sqrt{5}-113}{200}\approx -1.828378407$$

Steps Using the Quadratic Formula

Multiply 1.13 and 1.13 to get 1.2769.

$$x^{2}=1.2769-1.13x$$

Subtract 1.2769 from both sides.

$$x^{2}-1.2769=-1.13x$$

Add 1.13x to both sides.

$$x^{2}-1.2769+1.13x=0$$

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.

$$x^{2}+1.13x-1.2769=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 1.13 for b, and -1.2769 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1.13±\sqrt{1.13^{2}-4\left(-1.2769\right)}}{2}$$

Square 1.13 by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-1.13±\sqrt{1.2769-4\left(-1.2769\right)}}{2}$$

Multiply -4 times -1.2769.

$$x=\frac{-1.13±\sqrt{1.2769+5.1076}}{2}$$

Add 1.2769 to 5.1076 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-1.13±\sqrt{6.3845}}{2}$$

Take the square root of 6.3845.

$$x=\frac{-1.13±\frac{113\sqrt{5}}{100}}{2}$$

Now solve the equation x=\frac{-1.13±\frac{113\sqrt{5}}{100}}{2} when ± is plus. Add -1.13 to \frac{113\sqrt{5}}{100}.

$$x=\frac{113\sqrt{5}-113}{2\times 100}$$

Divide \frac{-113+113\sqrt{5}}{100} by 2.

$$x=\frac{113\sqrt{5}-113}{200}$$

Now solve the equation x=\frac{-1.13±\frac{113\sqrt{5}}{100}}{2} when ± is minus. Subtract \frac{113\sqrt{5}}{100} from -1.13.

$$x=\frac{-113\sqrt{5}-113}{2\times 100}$$

Divide \frac{-113-113\sqrt{5}}{100} by 2.

$$x=\frac{-113\sqrt{5}-113}{200}$$

The equation is now solved.

$$x=\frac{113\sqrt{5}-113}{200} x=\frac{-113\sqrt{5}-113}{200}$$

Steps for Completing the Square

Multiply 1.13 and 1.13 to get 1.2769.

$$x^{2}=1.2769-1.13x$$

Add 1.13x to both sides.

$$x^{2}+1.13x=1.2769$$

Divide 1.13, the coefficient of the x term, by 2 to get 0.565. Then add the square of 0.565 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+1.13x+0.565^{2}=1.2769+0.565^{2}$$

Square 0.565 by squaring both the numerator and the denominator of the fraction.

$$x^{2}+1.13x+0.319225=1.2769+0.319225$$

Add 1.2769 to 0.319225 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+1.13x+0.319225=1.596125$$

Factor x^{2}+1.13x+0.319225. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+0.565\right)^{2}=1.596125$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+0.565\right)^{2}}=\sqrt{1.596125}$$

Simplify.

$$x+0.565=\frac{113\sqrt{5}}{200} x+0.565=-\frac{113\sqrt{5}}{200}$$

Subtract 0.565 from both sides of the equation.

$$x=\frac{113\sqrt{5}-113}{200} x=\frac{-113\sqrt{5}-113}{200}$$