Solve 46.75x^2+28x=0

$$46.75 { x }^{ 2 } +28x=0$$

Solve for x

$$x=-\frac{112}{187}\approx -0.598930481$$

$$x=0$$

Steps Using Factoring

Factor out x.

$$x\left(46.75x+28\right)=0$$

To find equation solutions, solve x=0 and \frac{187x}{4}+28=0.

$$x=0 x=-\frac{112}{187}$$

Steps Using the Quadratic Formula

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.

$$46.75x^{2}+28x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 46.75 for a, 28 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-28±\sqrt{28^{2}}}{2\times 46.75}$$

Take the square root of 28^{2}.

$$x=\frac{-28±28}{2\times 46.75}$$

Multiply 2 times 46.75.

$$x=\frac{-28±28}{93.5}$$

Now solve the equation x=\frac{-28±28}{93.5} when ± is plus. Add -28 to 28.

$$x=\frac{0}{93.5}$$

Divide 0 by 93.5 by multiplying 0 by the reciprocal of 93.5.

$$x=0$$

Now solve the equation x=\frac{-28±28}{93.5} when ± is minus. Subtract 28 from -28.

$$x=-\frac{56}{93.5}$$

Divide -56 by 93.5 by multiplying -56 by the reciprocal of 93.5.

$$x=-\frac{112}{187}$$

The equation is now solved.

$$x=0 x=-\frac{112}{187}$$

Steps for Completing the Square

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$46.75x^{2}+28x=0$$

Divide both sides of the equation by 46.75, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{46.75x^{2}+28x}{46.75}=\frac{0}{46.75}$$

Dividing by 46.75 undoes the multiplication by 46.75.

$$x^{2}+\frac{28}{46.75}x=\frac{0}{46.75}$$

Divide 28 by 46.75 by multiplying 28 by the reciprocal of 46.75.

$$x^{2}+\frac{112}{187}x=\frac{0}{46.75}$$

Divide 0 by 46.75 by multiplying 0 by the reciprocal of 46.75.

$$x^{2}+\frac{112}{187}x=0$$

Divide \frac{112}{187}, the coefficient of the x term, by 2 to get \frac{56}{187}. Then add the square of \frac{56}{187} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{112}{187}x+\frac{56}{187}^{2}=\frac{56}{187}^{2}$$

Square \frac{56}{187} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{112}{187}x+\frac{3136}{34969}=\frac{3136}{34969}$$

Factor x^{2}+\frac{112}{187}x+\frac{3136}{34969}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{56}{187}\right)^{2}=\frac{3136}{34969}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{56}{187}\right)^{2}}=\sqrt{\frac{3136}{34969}}$$

Simplify.

$$x+\frac{56}{187}=\frac{56}{187} x+\frac{56}{187}=-\frac{56}{187}$$

Subtract \frac{56}{187} from both sides of the equation.

$$x=0 x=-\frac{112}{187}$$