Solve 0=-5x^2+35x

$$0 = - 5 x ^ { 2 } + 35 x$$

Solve for x

$$x=7$$

$$x=0$$

Steps Using Factoring

Swap sides so that all variable terms are on the left hand side.

$$-5x^{2}+35x=0$$

Factor out x.

$$x\left(-5x+35\right)=0$$

To find equation solutions, solve x=0 and -5x+35=0.

$$x=0 x=7$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$-5x^{2}+35x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -5 for a, 35 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-35±\sqrt{35^{2}}}{2\left(-5\right)}$$

Take the square root of 35^{2}.

$$x=\frac{-35±35}{2\left(-5\right)}$$

Multiply 2 times -5.

$$x=\frac{-35±35}{-10}$$

Now solve the equation x=\frac{-35±35}{-10} when ± is plus. Add -35 to 35.

$$x=\frac{0}{-10}$$

Divide 0 by -10.

$$x=0$$

Now solve the equation x=\frac{-35±35}{-10} when ± is minus. Subtract 35 from -35.

$$x=-\frac{70}{-10}$$

Divide -70 by -10.

$$x=7$$

The equation is now solved.

$$x=0 x=7$$

Steps for Completing the Square

Swap sides so that all variable terms are on the left hand side.

$$-5x^{2}+35x=0$$

Divide both sides by -5.

$$\frac{-5x^{2}+35x}{-5}=\frac{0}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$x^{2}+\frac{35}{-5}x=\frac{0}{-5}$$

Divide 35 by -5.

$$x^{2}-7x=\frac{0}{-5}$$

Divide 0 by -5.

$$x^{2}-7x=0$$

Divide -7, the coefficient of the x term, by 2 to get -\frac{7}{2}. Then add the square of -\frac{7}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=\left(-\frac{7}{2}\right)^{2}$$

Square -\frac{7}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-7x+\frac{49}{4}=\frac{49}{4}$$

Factor x^{2}-7x+\frac{49}{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}.

$$\left(x-\frac{7}{2}\right)^{2}=\frac{49}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Simplify.

$$x-\frac{7}{2}=\frac{7}{2} x-\frac{7}{2}=-\frac{7}{2}$$

Add \frac{7}{2} to both sides of the equation.

$$x=7 x=0$$