Solve 35x^2-35x=

$$35 x ^ { 2 } - 35 x =$$

Factor

$$35x\left(x-1\right)$$

Solution Steps

Factor out 35.

$$35\left(x^{2}-x\right)$$

Consider x^{2}-x. Factor out x.

$$x\left(x-1\right)$$

Rewrite the complete factored expression.

$$35x\left(x-1\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

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

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

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

Take the square root of \left(-35\right)^{2}.

$$x=\frac{-\left(-35\right)±35}{2\times 35}$$

The opposite of -35 is 35.

$$x=\frac{35±35}{2\times 35}$$

Multiply 2 times 35.

$$x=\frac{35±35}{70}$$

Now solve the equation x=\frac{35±35}{70} when ± is plus. Add 35 to 35.

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

Divide 70 by 70.

$$x=1$$

Now solve the equation x=\frac{35±35}{70} when ± is minus. Subtract 35 from 35.

$$x=\frac{0}{70}$$

Divide 0 by 70.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 1 for x_{1} and 0 for x_{2}.

$$35x^{2}-35x=35\left(x-1\right)x$$

Evaluate

$$35x\left(x-1\right)$$