Solve 3*(-6/5x)^2=-5x

$$3 \cdot ( - \frac { 6 } { 5 } x ) ^ { 2 } = - 5 x$$

Solve for x

$$x = -\frac{125}{108} = -1\frac{17}{108} \approx -1.157407407$$

$$x=0$$

Steps Using Factoring

Expand \left(-\frac{6}{5}x\right)^{2}.

$$3\left(-\frac{6}{5}\right)^{2}x^{2}=-5x$$

Calculate -\frac{6}{5} to the power of 2 and get \frac{36}{25}.

$$3\times \frac{36}{25}x^{2}=-5x$$

Multiply 3 and \frac{36}{25} to get \frac{108}{25}.

$$\frac{108}{25}x^{2}=-5x$$

Add 5x to both sides.

$$\frac{108}{25}x^{2}+5x=0$$

Factor out x.

$$x\left(\frac{108}{25}x+5\right)=0$$

To find equation solutions, solve x=0 and \frac{108x}{25}+5=0.

$$x=0 x=-\frac{125}{108}$$

Steps Using the Quadratic Formula

Expand \left(-\frac{6}{5}x\right)^{2}.

$$3\left(-\frac{6}{5}\right)^{2}x^{2}=-5x$$

Calculate -\frac{6}{5} to the power of 2 and get \frac{36}{25}.

$$3\times \frac{36}{25}x^{2}=-5x$$

Multiply 3 and \frac{36}{25} to get \frac{108}{25}.

$$\frac{108}{25}x^{2}=-5x$$

Add 5x to both sides.

$$\frac{108}{25}x^{2}+5x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{108}{25} for a, 5 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}}}{2\times \frac{108}{25}}$$

Take the square root of 5^{2}.

$$x=\frac{-5±5}{2\times \frac{108}{25}}$$

Multiply 2 times \frac{108}{25}.

$$x=\frac{-5±5}{\frac{216}{25}}$$

Now solve the equation x=\frac{-5±5}{\frac{216}{25}} when ± is plus. Add -5 to 5.

$$x=\frac{0}{\frac{216}{25}}$$

Divide 0 by \frac{216}{25} by multiplying 0 by the reciprocal of \frac{216}{25}.

$$x=0$$

Now solve the equation x=\frac{-5±5}{\frac{216}{25}} when ± is minus. Subtract 5 from -5.

$$x=-\frac{10}{\frac{216}{25}}$$

Divide -10 by \frac{216}{25} by multiplying -10 by the reciprocal of \frac{216}{25}.

$$x=-\frac{125}{108}$$

The equation is now solved.

$$x=0 x=-\frac{125}{108}$$

Steps for Completing the Square

Expand \left(-\frac{6}{5}x\right)^{2}.

$$3\left(-\frac{6}{5}\right)^{2}x^{2}=-5x$$

Calculate -\frac{6}{5} to the power of 2 and get \frac{36}{25}.

$$3\times \frac{36}{25}x^{2}=-5x$$

Multiply 3 and \frac{36}{25} to get \frac{108}{25}.

$$\frac{108}{25}x^{2}=-5x$$

Add 5x to both sides.

$$\frac{108}{25}x^{2}+5x=0$$

Divide both sides of the equation by \frac{108}{25}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{108}{25}x^{2}+5x}{\frac{108}{25}}=\frac{0}{\frac{108}{25}}$$

Dividing by \frac{108}{25} undoes the multiplication by \frac{108}{25}.

$$x^{2}+\frac{5}{\frac{108}{25}}x=\frac{0}{\frac{108}{25}}$$

Divide 5 by \frac{108}{25} by multiplying 5 by the reciprocal of \frac{108}{25}.

$$x^{2}+\frac{125}{108}x=\frac{0}{\frac{108}{25}}$$

Divide 0 by \frac{108}{25} by multiplying 0 by the reciprocal of \frac{108}{25}.

$$x^{2}+\frac{125}{108}x=0$$

Divide \frac{125}{108}, the coefficient of the x term, by 2 to get \frac{125}{216}. Then add the square of \frac{125}{216} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{125}{108}x+\left(\frac{125}{216}\right)^{2}=\left(\frac{125}{216}\right)^{2}$$

Square \frac{125}{216} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{125}{108}x+\frac{15625}{46656}=\frac{15625}{46656}$$

Factor x^{2}+\frac{125}{108}x+\frac{15625}{46656}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{125}{216}\right)^{2}=\frac{15625}{46656}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{125}{216}\right)^{2}}=\sqrt{\frac{15625}{46656}}$$

Simplify.

$$x+\frac{125}{216}=\frac{125}{216} x+\frac{125}{216}=-\frac{125}{216}$$

Subtract \frac{125}{216} from both sides of the equation.

$$x=0 x=-\frac{125}{108}$$