Solve x^2+3x(25div18)=2x^2

$$x ^ { 2 } + 3 x ( 25 \div 18 ) = 2 x ^ { 2 }$$

Solve for x

$$x = \frac{25}{6} = 4\frac{1}{6} \approx 4.166666667$$

$$x=0$$

Steps Using Factoring

Multiply 3 and \frac{25}{18} to get \frac{25}{6}.

$$x^{2}+\frac{25}{6}x=2x^{2}$$

Subtract 2x^{2} from both sides.

$$x^{2}+\frac{25}{6}x-2x^{2}=0$$

Combine x^{2} and -2x^{2} to get -x^{2}.

$$-x^{2}+\frac{25}{6}x=0$$

Factor out x.

$$x\left(-x+\frac{25}{6}\right)=0$$

To find equation solutions, solve x=0 and -x+\frac{25}{6}=0.

$$x=0 x=\frac{25}{6}$$

Steps Using the Quadratic Formula

Multiply 3 and \frac{25}{18} to get \frac{25}{6}.

$$x^{2}+\frac{25}{6}x=2x^{2}$$

Subtract 2x^{2} from both sides.

$$x^{2}+\frac{25}{6}x-2x^{2}=0$$

Combine x^{2} and -2x^{2} to get -x^{2}.

$$-x^{2}+\frac{25}{6}x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, \frac{25}{6} for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{25}{6}±\sqrt{\left(\frac{25}{6}\right)^{2}}}{2\left(-1\right)}$$

Take the square root of \left(\frac{25}{6}\right)^{2}.

$$x=\frac{-\frac{25}{6}±\frac{25}{6}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{-\frac{25}{6}±\frac{25}{6}}{-2}$$

Now solve the equation x=\frac{-\frac{25}{6}±\frac{25}{6}}{-2} when ± is plus. Add -\frac{25}{6} to \frac{25}{6} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0}{-2}$$

Divide 0 by -2.

$$x=0$$

Now solve the equation x=\frac{-\frac{25}{6}±\frac{25}{6}}{-2} when ± is minus. Subtract \frac{25}{6} from -\frac{25}{6} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{\frac{25}{3}}{-2}$$

Divide -\frac{25}{3} by -2.

$$x=\frac{25}{6}$$

The equation is now solved.

$$x=0 x=\frac{25}{6}$$

Steps for Completing the Square

Multiply 3 and \frac{25}{18} to get \frac{25}{6}.

$$x^{2}+\frac{25}{6}x=2x^{2}$$

Subtract 2x^{2} from both sides.

$$x^{2}+\frac{25}{6}x-2x^{2}=0$$

Combine x^{2} and -2x^{2} to get -x^{2}.

$$-x^{2}+\frac{25}{6}x=0$$

Divide both sides by -1.

$$\frac{-x^{2}+\frac{25}{6}x}{-1}=\frac{0}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x^{2}+\frac{\frac{25}{6}}{-1}x=\frac{0}{-1}$$

Divide \frac{25}{6} by -1.

$$x^{2}-\frac{25}{6}x=\frac{0}{-1}$$

Divide 0 by -1.

$$x^{2}-\frac{25}{6}x=0$$

Divide -\frac{25}{6}, the coefficient of the x term, by 2 to get -\frac{25}{12}. Then add the square of -\frac{25}{12} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{25}{6}x+\left(-\frac{25}{12}\right)^{2}=\left(-\frac{25}{12}\right)^{2}$$

Square -\frac{25}{12} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{25}{6}x+\frac{625}{144}=\frac{625}{144}$$

Factor x^{2}-\frac{25}{6}x+\frac{625}{144}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{25}{12}\right)^{2}=\frac{625}{144}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{25}{12}\right)^{2}}=\sqrt{\frac{625}{144}}$$

Simplify.

$$x-\frac{25}{12}=\frac{25}{12} x-\frac{25}{12}=-\frac{25}{12}$$

Add \frac{25}{12} to both sides of the equation.

$$x=\frac{25}{6} x=0$$