Solve 7xx-5x=0

$$7 x x - 5 x = 0$$

Solve for x

$$x=\frac{5}{7}\approx 0.714285714$$

$$x=0$$

Steps Using Factoring

Factor out x.

$$x\left(7x-5\right)=0$$

To find equation solutions, solve x=0 and 7x-5=0.

$$x=0 x=\frac{5}{7}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, -5 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}}}{2\times 7}$$

Take the square root of \left(-5\right)^{2}.

$$x=\frac{-\left(-5\right)±5}{2\times 7}$$

The opposite of -5 is 5.

$$x=\frac{5±5}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{5±5}{14}$$

Now solve the equation x=\frac{5±5}{14} when ± is plus. Add 5 to 5.

$$x=\frac{10}{14}$$

Reduce the fraction \frac{10}{14} to lowest terms by extracting and canceling out 2.

$$x=\frac{5}{7}$$

Now solve the equation x=\frac{5±5}{14} when ± is minus. Subtract 5 from 5.

$$x=\frac{0}{14}$$

Divide 0 by 14.

$$x=0$$

The equation is now solved.

$$x=\frac{5}{7} x=0$$

Steps for Completing the Square

Multiply x and x to get x^{2}.

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

Divide both sides by 7.

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

Dividing by 7 undoes the multiplication by 7.

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

Divide 0 by 7.

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

Divide -\frac{5}{7}, the coefficient of the x term, by 2 to get -\frac{5}{14}. Then add the square of -\frac{5}{14} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{5}{7}x+\left(-\frac{5}{14}\right)^{2}=\left(-\frac{5}{14}\right)^{2}$$

Square -\frac{5}{14} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{5}{7}x+\frac{25}{196}=\frac{25}{196}$$

Factor x^{2}-\frac{5}{7}x+\frac{25}{196}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{5}{14}\right)^{2}=\frac{25}{196}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{5}{14}\right)^{2}}=\sqrt{\frac{25}{196}}$$

Simplify.

$$x-\frac{5}{14}=\frac{5}{14} x-\frac{5}{14}=-\frac{5}{14}$$

Add \frac{5}{14} to both sides of the equation.

$$x=\frac{5}{7} x=0$$