Solve 1.072=(2x+.15)*(2x+.15)

$$1.072=(2x+.15) \times (2x+.15)$$

Solve for x

$$x=\frac{\sqrt{670}}{50}-0.075\approx 0.442687164$$

$$x=-\frac{\sqrt{670}}{50}-0.075\approx -0.592687164$$

Steps Using the Quadratic Formula

Multiply 2x+0.15 and 2x+0.15 to get \left(2x+0.15\right)^{2}.

$$1.072=\left(2x+0.15\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+0.15\right)^{2}.

$$1.072=4x^{2}+0.6x+0.0225$$

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

$$4x^{2}+0.6x+0.0225=1.072$$

Subtract 1.072 from both sides.

$$4x^{2}+0.6x+0.0225-1.072=0$$

Subtract 1.072 from 0.0225 to get -1.0495.

$$4x^{2}+0.6x-1.0495=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0.6 for b, and -1.0495 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-0.6±\sqrt{0.6^{2}-4\times 4\left(-1.0495\right)}}{2\times 4}$$

Square 0.6 by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-0.6±\sqrt{0.36-4\times 4\left(-1.0495\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{-0.6±\sqrt{0.36-16\left(-1.0495\right)}}{2\times 4}$$

Multiply -16 times -1.0495.

$$x=\frac{-0.6±\sqrt{0.36+16.792}}{2\times 4}$$

Add 0.36 to 16.792 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-0.6±\sqrt{17.152}}{2\times 4}$$

Take the square root of 17.152.

$$x=\frac{-0.6±\frac{4\sqrt{670}}{25}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{-0.6±\frac{4\sqrt{670}}{25}}{8}$$

Now solve the equation x=\frac{-0.6±\frac{4\sqrt{670}}{25}}{8} when ± is plus. Add -0.6 to \frac{4\sqrt{670}}{25}.

$$x=\frac{\frac{4\sqrt{670}}{25}-\frac{3}{5}}{8}$$

Divide -\frac{3}{5}+\frac{4\sqrt{670}}{25} by 8.

$$x=\frac{\sqrt{670}}{50}-\frac{3}{40}$$

Now solve the equation x=\frac{-0.6±\frac{4\sqrt{670}}{25}}{8} when ± is minus. Subtract \frac{4\sqrt{670}}{25} from -0.6.

$$x=\frac{-\frac{4\sqrt{670}}{25}-\frac{3}{5}}{8}$$

Divide -\frac{3}{5}-\frac{4\sqrt{670}}{25} by 8.

$$x=-\frac{\sqrt{670}}{50}-\frac{3}{40}$$

The equation is now solved.

$$x=\frac{\sqrt{670}}{50}-\frac{3}{40} x=-\frac{\sqrt{670}}{50}-\frac{3}{40}$$

Steps for Completing the Square

Multiply 2x+0.15 and 2x+0.15 to get \left(2x+0.15\right)^{2}.

$$1.072=\left(2x+0.15\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+0.15\right)^{2}.

$$1.072=4x^{2}+0.6x+0.0225$$

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

$$4x^{2}+0.6x+0.0225=1.072$$

Subtract 0.0225 from both sides.

$$4x^{2}+0.6x=1.072-0.0225$$

Subtract 0.0225 from 1.072 to get 1.0495.

$$4x^{2}+0.6x=1.0495$$

Divide both sides by 4.

$$\frac{4x^{2}+0.6x}{4}=\frac{1.0495}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x^{2}+\frac{0.6}{4}x=\frac{1.0495}{4}$$

Divide 0.6 by 4.

$$x^{2}+0.15x=\frac{1.0495}{4}$$

Divide 1.0495 by 4.

$$x^{2}+0.15x=0.262375$$

Divide 0.15, the coefficient of the x term, by 2 to get 0.075. Then add the square of 0.075 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+0.15x+0.075^{2}=0.262375+0.075^{2}$$

Square 0.075 by squaring both the numerator and the denominator of the fraction.

$$x^{2}+0.15x+0.005625=0.262375+0.005625$$

Add 0.262375 to 0.005625 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+0.15x+0.005625=0.268$$

Factor x^{2}+0.15x+0.005625. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+0.075\right)^{2}=0.268$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+0.075\right)^{2}}=\sqrt{0.268}$$

Simplify.

$$x+0.075=\frac{\sqrt{670}}{50} x+0.075=-\frac{\sqrt{670}}{50}$$

Subtract 0.075 from both sides of the equation.

$$x=\frac{\sqrt{670}}{50}-\frac{3}{40} x=-\frac{\sqrt{670}}{50}-\frac{3}{40}$$