Solve 28x=-67.2/x

$$28x= \frac{ -67.2 }{ x }$$

Solve for x (complex solution)

$$x=-\frac{i\times 2\sqrt{15}}{5}\approx -0-1.549193338i$$

$$x=\frac{i\times 2\sqrt{15}}{5}\approx 1.549193338i$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$28xx=-67.2$$

Multiply x and x to get x^{2}.

$$28x^{2}=-67.2$$

Divide both sides by 28.

$$x^{2}=\frac{-67.2}{28}$$

Expand \frac{-67.2}{28} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{-672}{280}$$

Reduce the fraction \frac{-672}{280} to lowest terms by extracting and canceling out 56.

$$x^{2}=-\frac{12}{5}$$

The equation is now solved.

$$x=\frac{2\sqrt{15}i}{5} x=-\frac{2\sqrt{15}i}{5}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$28xx=-67.2$$

Multiply x and x to get x^{2}.

$$28x^{2}=-67.2$$

Add 67.2 to both sides.

$$28x^{2}+67.2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 28 for a, 0 for b, and 67.2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 28\times 67.2}}{2\times 28}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 28\times 67.2}}{2\times 28}$$

Multiply -4 times 28.

$$x=\frac{0±\sqrt{-112\times 67.2}}{2\times 28}$$

Multiply -112 times 67.2.

$$x=\frac{0±\sqrt{-7526.4}}{2\times 28}$$

Take the square root of -7526.4.

$$x=\frac{0±\frac{112\sqrt{15}i}{5}}{2\times 28}$$

Multiply 2 times 28.

$$x=\frac{0±\frac{112\sqrt{15}i}{5}}{56}$$

Now solve the equation x=\frac{0±\frac{112\sqrt{15}i}{5}}{56} when ± is plus.

$$x=\frac{2\sqrt{15}i}{5}$$

Now solve the equation x=\frac{0±\frac{112\sqrt{15}i}{5}}{56} when ± is minus.

$$x=-\frac{2\sqrt{15}i}{5}$$

The equation is now solved.

$$x=\frac{2\sqrt{15}i}{5} x=-\frac{2\sqrt{15}i}{5}$$