Solve 4=20y^2+36.8y

$$4 = 20 y ^ { 2 } + 36.8 y$$

Solve for y

$$y=\frac{\sqrt{654}-23}{25}\approx 0.102936948$$

$$y=\frac{-\sqrt{654}-23}{25}\approx -1.942936948$$

Steps Using the Quadratic Formula

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

$$20y^{2}+36.8y=4$$

Subtract 4 from both sides.

$$20y^{2}+36.8y-4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, 36.8 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-36.8±\sqrt{36.8^{2}-4\times 20\left(-4\right)}}{2\times 20}$$

Square 36.8 by squaring both the numerator and the denominator of the fraction.

$$y=\frac{-36.8±\sqrt{1354.24-4\times 20\left(-4\right)}}{2\times 20}$$

Multiply -4 times 20.

$$y=\frac{-36.8±\sqrt{1354.24-80\left(-4\right)}}{2\times 20}$$

Multiply -80 times -4.

$$y=\frac{-36.8±\sqrt{1354.24+320}}{2\times 20}$$

Add 1354.24 to 320.

$$y=\frac{-36.8±\sqrt{1674.24}}{2\times 20}$$

Take the square root of 1674.24.

$$y=\frac{-36.8±\frac{8\sqrt{654}}{5}}{2\times 20}$$

Multiply 2 times 20.

$$y=\frac{-36.8±\frac{8\sqrt{654}}{5}}{40}$$

Now solve the equation y=\frac{-36.8±\frac{8\sqrt{654}}{5}}{40} when ± is plus. Add -36.8 to \frac{8\sqrt{654}}{5}.

$$y=\frac{8\sqrt{654}-184}{5\times 40}$$

Divide \frac{-184+8\sqrt{654}}{5} by 40.

$$y=\frac{\sqrt{654}-23}{25}$$

Now solve the equation y=\frac{-36.8±\frac{8\sqrt{654}}{5}}{40} when ± is minus. Subtract \frac{8\sqrt{654}}{5} from -36.8.

$$y=\frac{-8\sqrt{654}-184}{5\times 40}$$

Divide \frac{-184-8\sqrt{654}}{5} by 40.

$$y=\frac{-\sqrt{654}-23}{25}$$

The equation is now solved.

$$y=\frac{\sqrt{654}-23}{25} y=\frac{-\sqrt{654}-23}{25}$$

Steps for Completing the Square

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

$$20y^{2}+36.8y=4$$

Divide both sides by 20.

$$\frac{20y^{2}+36.8y}{20}=\frac{4}{20}$$

Dividing by 20 undoes the multiplication by 20.

$$y^{2}+\frac{36.8}{20}y=\frac{4}{20}$$

Divide 36.8 by 20.

$$y^{2}+1.84y=\frac{4}{20}$$

Reduce the fraction \frac{4}{20} to lowest terms by extracting and canceling out 4.

$$y^{2}+1.84y=\frac{1}{5}$$

Divide 1.84, the coefficient of the x term, by 2 to get 0.92. Then add the square of 0.92 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$y^{2}+1.84y+0.92^{2}=\frac{1}{5}+0.92^{2}$$

Square 0.92 by squaring both the numerator and the denominator of the fraction.

$$y^{2}+1.84y+0.8464=\frac{1}{5}+0.8464$$

Add \frac{1}{5} to 0.8464 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$y^{2}+1.84y+0.8464=\frac{654}{625}$$

Factor y^{2}+1.84y+0.8464. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(y+0.92\right)^{2}=\frac{654}{625}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(y+0.92\right)^{2}}=\sqrt{\frac{654}{625}}$$

Simplify.

$$y+0.92=\frac{\sqrt{654}}{25} y+0.92=-\frac{\sqrt{654}}{25}$$

Subtract 0.92 from both sides of the equation.

$$y=\frac{\sqrt{654}-23}{25} y=\frac{-\sqrt{654}-23}{25}$$