Solve 2x^2-6x*5=0

$$2 x ^ { 2 } - 6 x \cdot 5 = 0$$

Solve for x

$$x=15$$

$$x=0$$

Steps Using Factoring

Multiply 6 and 5 to get 30.

$$2x^{2}-30x=0$$

Factor out x.

$$x\left(2x-30\right)=0$$

To find equation solutions, solve x=0 and 2x-30=0.

$$x=0 x=15$$

Steps Using the Quadratic Formula

Multiply 6 and 5 to get 30.

$$2x^{2}-30x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, -30 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-30\right)±\sqrt{\left(-30\right)^{2}}}{2\times 2}$$

Take the square root of \left(-30\right)^{2}.

$$x=\frac{-\left(-30\right)±30}{2\times 2}$$

The opposite of -30 is 30.

$$x=\frac{30±30}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{30±30}{4}$$

Now solve the equation x=\frac{30±30}{4} when ± is plus. Add 30 to 30.

$$x=\frac{60}{4}$$

Divide 60 by 4.

$$x=15$$

Now solve the equation x=\frac{30±30}{4} when ± is minus. Subtract 30 from 30.

$$x=\frac{0}{4}$$

Divide 0 by 4.

$$x=0$$

The equation is now solved.

$$x=15 x=0$$

Steps for Completing the Square

Multiply 6 and 5 to get 30.

$$2x^{2}-30x=0$$

Divide both sides by 2.

$$\frac{2x^{2}-30x}{2}=\frac{0}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\left(-\frac{30}{2}\right)x=\frac{0}{2}$$

Divide -30 by 2.

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

Divide 0 by 2.

$$x^{2}-15x=0$$

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

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

Square -\frac{15}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-15x+\frac{225}{4}=\frac{225}{4}$$

Factor x^{2}-15x+\frac{225}{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}.

$$\left(x-\frac{15}{2}\right)^{2}=\frac{225}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{15}{2}\right)^{2}}=\sqrt{\frac{225}{4}}$$

Simplify.

$$x-\frac{15}{2}=\frac{15}{2} x-\frac{15}{2}=-\frac{15}{2}$$

Add \frac{15}{2} to both sides of the equation.

$$x=15 x=0$$