Solve -2/j+7=j/5

$$\frac { - 2 } { j + 7 } = \frac { j } { 5 }$$

Solve for j

$$j=-5$$

$$j=-2$$

Steps Using the Quadratic Formula

Variable j cannot be equal to -7 since division by zero is not defined. Multiply both sides of the equation by 5\left(j+7\right), the least common multiple of j+7,5.

$$5\left(-2\right)=\left(j+7\right)j$$

Multiply 5 and -2 to get -10.

$$-10=\left(j+7\right)j$$

Use the distributive property to multiply j+7 by j.

$$-10=j^{2}+7j$$

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

$$j^{2}+7j=-10$$

Add 10 to both sides.

$$j^{2}+7j+10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 7 for b, and 10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$j=\frac{-7±\sqrt{7^{2}-4\times 10}}{2}$$

Square 7.

$$j=\frac{-7±\sqrt{49-4\times 10}}{2}$$

Multiply -4 times 10.

$$j=\frac{-7±\sqrt{49-40}}{2}$$

Add 49 to -40.

$$j=\frac{-7±\sqrt{9}}{2}$$

Take the square root of 9.

$$j=\frac{-7±3}{2}$$

Now solve the equation j=\frac{-7±3}{2} when ± is plus. Add -7 to 3.

$$j=-\frac{4}{2}$$

Divide -4 by 2.

$$j=-2$$

Now solve the equation j=\frac{-7±3}{2} when ± is minus. Subtract 3 from -7.

$$j=-\frac{10}{2}$$

Divide -10 by 2.

$$j=-5$$

The equation is now solved.

$$j=-2 j=-5$$

Steps for Completing the Square

Variable j cannot be equal to -7 since division by zero is not defined. Multiply both sides of the equation by 5\left(j+7\right), the least common multiple of j+7,5.

$$5\left(-2\right)=\left(j+7\right)j$$

Multiply 5 and -2 to get -10.

$$-10=\left(j+7\right)j$$

Use the distributive property to multiply j+7 by j.

$$-10=j^{2}+7j$$

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

$$j^{2}+7j=-10$$

Divide 7, the coefficient of the x term, by 2 to get \frac{7}{2}. Then add the square of \frac{7}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$j^{2}+7j+\left(\frac{7}{2}\right)^{2}=-10+\left(\frac{7}{2}\right)^{2}$$

Square \frac{7}{2} by squaring both the numerator and the denominator of the fraction.

$$j^{2}+7j+\frac{49}{4}=-10+\frac{49}{4}$$

Add -10 to \frac{49}{4}.

$$j^{2}+7j+\frac{49}{4}=\frac{9}{4}$$

Factor j^{2}+7j+\frac{49}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(j+\frac{7}{2}\right)^{2}=\frac{9}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(j+\frac{7}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Simplify.

$$j+\frac{7}{2}=\frac{3}{2} j+\frac{7}{2}=-\frac{3}{2}$$

Subtract \frac{7}{2} from both sides of the equation.

$$j=-2 j=-5$$