Solve -7u^2+34u

$$- 7 u ^ { 2 } + 34 u$$

Factor

$$u\left(34-7u\right)$$

Solution Steps

Factor out u.

$$u\left(-7u+34\right)$$

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.

$$-7u^{2}+34u=0$$

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.

$$u=\frac{-34±\sqrt{34^{2}}}{2\left(-7\right)}$$

Take the square root of 34^{2}.

$$u=\frac{-34±34}{2\left(-7\right)}$$

Multiply 2 times -7.

$$u=\frac{-34±34}{-14}$$

Now solve the equation u=\frac{-34±34}{-14} when ± is plus. Add -34 to 34.

$$u=\frac{0}{-14}$$

Divide 0 by -14.

$$u=0$$

Now solve the equation u=\frac{-34±34}{-14} when ± is minus. Subtract 34 from -34.

$$u=-\frac{68}{-14}$$

Reduce the fraction \frac{-68}{-14} to lowest terms by extracting and canceling out 2.

$$u=\frac{34}{7}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and \frac{34}{7} for x_{2}.

$$-7u^{2}+34u=-7u\left(u-\frac{34}{7}\right)$$

Subtract \frac{34}{7} from u by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$-7u^{2}+34u=-7u\times \frac{-7u+34}{-7}$$

Cancel out 7, the greatest common factor in -7 and -7.

$$-7u^{2}+34u=u\left(-7u+34\right)$$

Evaluate

$$u\left(34-7u\right)$$