Solve 26.2x^2=3x

$$26.2 x ^ { 2 } = 3 x$$

Solve for x

$$x=\frac{15}{131}\approx 0.114503817$$

$$x=0$$

Steps Using Factoring

Subtract 3x from both sides.

$$26.2x^{2}-3x=0$$

Factor out x.

$$x\left(26.2x-3\right)=0$$

To find equation solutions, solve x=0 and \frac{131x}{5}-3=0.

$$x=0 x=\frac{15}{131}$$

Steps Using the Quadratic Formula

Subtract 3x from both sides.

$$26.2x^{2}-3x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 26.2 for a, -3 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}}}{2\times 26.2}$$

Take the square root of \left(-3\right)^{2}.

$$x=\frac{-\left(-3\right)±3}{2\times 26.2}$$

The opposite of -3 is 3.

$$x=\frac{3±3}{2\times 26.2}$$

Multiply 2 times 26.2.

$$x=\frac{3±3}{52.4}$$

Now solve the equation x=\frac{3±3}{52.4} when ± is plus. Add 3 to 3.

$$x=\frac{6}{52.4}$$

Divide 6 by 52.4 by multiplying 6 by the reciprocal of 52.4.

$$x=\frac{15}{131}$$

Now solve the equation x=\frac{3±3}{52.4} when ± is minus. Subtract 3 from 3.

$$x=\frac{0}{52.4}$$

Divide 0 by 52.4 by multiplying 0 by the reciprocal of 52.4.

$$x=0$$

The equation is now solved.

$$x=\frac{15}{131} x=0$$

Steps for Completing the Square

Subtract 3x from both sides.

$$26.2x^{2}-3x=0$$

Divide both sides of the equation by 26.2, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{26.2x^{2}-3x}{26.2}=\frac{0}{26.2}$$

Dividing by 26.2 undoes the multiplication by 26.2.

$$x^{2}+\left(-\frac{3}{26.2}\right)x=\frac{0}{26.2}$$

Divide -3 by 26.2 by multiplying -3 by the reciprocal of 26.2.

$$x^{2}-\frac{15}{131}x=\frac{0}{26.2}$$

Divide 0 by 26.2 by multiplying 0 by the reciprocal of 26.2.

$$x^{2}-\frac{15}{131}x=0$$

Divide -\frac{15}{131}, the coefficient of the x term, by 2 to get -\frac{15}{262}. Then add the square of -\frac{15}{262} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{15}{131}x+\left(-\frac{15}{262}\right)^{2}=\left(-\frac{15}{262}\right)^{2}$$

Square -\frac{15}{262} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{15}{131}x+\frac{225}{68644}=\frac{225}{68644}$$

Factor x^{2}-\frac{15}{131}x+\frac{225}{68644}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{15}{262}\right)^{2}=\frac{225}{68644}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{15}{262}\right)^{2}}=\sqrt{\frac{225}{68644}}$$

Simplify.

$$x-\frac{15}{262}=\frac{15}{262} x-\frac{15}{262}=-\frac{15}{262}$$

Add \frac{15}{262} to both sides of the equation.

$$x=\frac{15}{131} x=0$$