Solve a^2+3146a=87a/142

$$a ^ { 2 } + 3146 a = \frac { 87 a } { 142 }$$

Solve for a

$$a = -\frac{446645}{142} = -3145\frac{55}{142} \approx -3145.387323944$$

$$a=0$$

Steps Using Factoring

Multiply both sides of the equation by 142.

$$142a^{2}+446732a=87a$$

Subtract 87a from both sides.

$$142a^{2}+446732a-87a=0$$

Combine 446732a and -87a to get 446645a.

$$142a^{2}+446645a=0$$

Factor out a.

$$a\left(142a+446645\right)=0$$

To find equation solutions, solve a=0 and 142a+446645=0.

$$a=0 a=-\frac{446645}{142}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 142.

$$142a^{2}+446732a=87a$$

Subtract 87a from both sides.

$$142a^{2}+446732a-87a=0$$

Combine 446732a and -87a to get 446645a.

$$142a^{2}+446645a=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 142 for a, 446645 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-446645±\sqrt{446645^{2}}}{2\times 142}$$

Take the square root of 446645^{2}.

$$a=\frac{-446645±446645}{2\times 142}$$

Multiply 2 times 142.

$$a=\frac{-446645±446645}{284}$$

Now solve the equation a=\frac{-446645±446645}{284} when ± is plus. Add -446645 to 446645.

$$a=\frac{0}{284}$$

Divide 0 by 284.

$$a=0$$

Now solve the equation a=\frac{-446645±446645}{284} when ± is minus. Subtract 446645 from -446645.

$$a=-\frac{893290}{284}$$

Reduce the fraction \frac{-893290}{284} to lowest terms by extracting and canceling out 2.

$$a=-\frac{446645}{142}$$

The equation is now solved.

$$a=0 a=-\frac{446645}{142}$$

Steps for Completing the Square

Multiply both sides of the equation by 142.

$$142a^{2}+446732a=87a$$

Subtract 87a from both sides.

$$142a^{2}+446732a-87a=0$$

Combine 446732a and -87a to get 446645a.

$$142a^{2}+446645a=0$$

Divide both sides by 142.

$$\frac{142a^{2}+446645a}{142}=\frac{0}{142}$$

Dividing by 142 undoes the multiplication by 142.

$$a^{2}+\frac{446645}{142}a=\frac{0}{142}$$

Divide 0 by 142.

$$a^{2}+\frac{446645}{142}a=0$$

Divide \frac{446645}{142}, the coefficient of the x term, by 2 to get \frac{446645}{284}. Then add the square of \frac{446645}{284} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$a^{2}+\frac{446645}{142}a+\left(\frac{446645}{284}\right)^{2}=\left(\frac{446645}{284}\right)^{2}$$

Square \frac{446645}{284} by squaring both the numerator and the denominator of the fraction.

$$a^{2}+\frac{446645}{142}a+\frac{199491756025}{80656}=\frac{199491756025}{80656}$$

Factor a^{2}+\frac{446645}{142}a+\frac{199491756025}{80656}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(a+\frac{446645}{284}\right)^{2}=\frac{199491756025}{80656}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(a+\frac{446645}{284}\right)^{2}}=\sqrt{\frac{199491756025}{80656}}$$

Simplify.

$$a+\frac{446645}{284}=\frac{446645}{284} a+\frac{446645}{284}=-\frac{446645}{284}$$

Subtract \frac{446645}{284} from both sides of the equation.

$$a=0 a=-\frac{446645}{142}$$