Solve 3.85=(2x+.2)*(2x+.3)

$$3.85=(2x+.2) \times (2x+.3)$$

Solve for x

$$x=\frac{\sqrt{1541}}{40}-0.125\approx 0.856389321$$

$$x=-\frac{\sqrt{1541}}{40}-0.125\approx -1.106389321$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x+0.2 by 2x+0.3 and combine like terms.

$$3.85=4x^{2}+x+0.06$$

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

$$4x^{2}+x+0.06=3.85$$

Subtract 3.85 from both sides.

$$4x^{2}+x+0.06-3.85=0$$

Subtract 3.85 from 0.06 to get -3.79.

$$4x^{2}+x-3.79=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 1 for b, and -3.79 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1±\sqrt{1^{2}-4\times 4\left(-3.79\right)}}{2\times 4}$$

Square 1.

$$x=\frac{-1±\sqrt{1-4\times 4\left(-3.79\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{-1±\sqrt{1-16\left(-3.79\right)}}{2\times 4}$$

Multiply -16 times -3.79.

$$x=\frac{-1±\sqrt{1+60.64}}{2\times 4}$$

Add 1 to 60.64.

$$x=\frac{-1±\sqrt{61.64}}{2\times 4}$$

Take the square root of 61.64.

$$x=\frac{-1±\frac{\sqrt{1541}}{5}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{-1±\frac{\sqrt{1541}}{5}}{8}$$

Now solve the equation x=\frac{-1±\frac{\sqrt{1541}}{5}}{8} when ± is plus. Add -1 to \frac{\sqrt{1541}}{5}.

$$x=\frac{\frac{\sqrt{1541}}{5}-1}{8}$$

Divide -1+\frac{\sqrt{1541}}{5} by 8.

$$x=\frac{\sqrt{1541}}{40}-\frac{1}{8}$$

Now solve the equation x=\frac{-1±\frac{\sqrt{1541}}{5}}{8} when ± is minus. Subtract \frac{\sqrt{1541}}{5} from -1.

$$x=\frac{-\frac{\sqrt{1541}}{5}-1}{8}$$

Divide -1-\frac{\sqrt{1541}}{5} by 8.

$$x=-\frac{\sqrt{1541}}{40}-\frac{1}{8}$$

The equation is now solved.

$$x=\frac{\sqrt{1541}}{40}-\frac{1}{8} x=-\frac{\sqrt{1541}}{40}-\frac{1}{8}$$

Steps for Completing the Square

Use the distributive property to multiply 2x+0.2 by 2x+0.3 and combine like terms.

$$3.85=4x^{2}+x+0.06$$

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

$$4x^{2}+x+0.06=3.85$$

Subtract 0.06 from both sides.

$$4x^{2}+x=3.85-0.06$$

Subtract 0.06 from 3.85 to get 3.79.

$$4x^{2}+x=3.79$$

Divide both sides by 4.

$$\frac{4x^{2}+x}{4}=\frac{3.79}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x^{2}+\frac{1}{4}x=\frac{3.79}{4}$$

Divide 3.79 by 4.

$$x^{2}+\frac{1}{4}x=0.9475$$

Divide \frac{1}{4}, the coefficient of the x term, by 2 to get \frac{1}{8}. Then add the square of \frac{1}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{1}{4}x+\left(\frac{1}{8}\right)^{2}=0.9475+\left(\frac{1}{8}\right)^{2}$$

Square \frac{1}{8} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{1}{4}x+\frac{1}{64}=0.9475+\frac{1}{64}$$

Add 0.9475 to \frac{1}{64} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{1}{4}x+\frac{1}{64}=\frac{1541}{1600}$$

Factor x^{2}+\frac{1}{4}x+\frac{1}{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}.

$$\left(x+\frac{1}{8}\right)^{2}=\frac{1541}{1600}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{1}{8}\right)^{2}}=\sqrt{\frac{1541}{1600}}$$

Simplify.

$$x+\frac{1}{8}=\frac{\sqrt{1541}}{40} x+\frac{1}{8}=-\frac{\sqrt{1541}}{40}$$

Subtract \frac{1}{8} from both sides of the equation.

$$x=\frac{\sqrt{1541}}{40}-\frac{1}{8} x=-\frac{\sqrt{1541}}{40}-\frac{1}{8}$$