Solve 9x^2-54x)

$$9 { x }^{ 2 } -54x)$$

Factor

$$9x\left(x-6\right)$$

Solution Steps

Factor out 9.

$$9\left(x^{2}-6x\right)$$

Consider x^{2}-6x. Factor out x.

$$x\left(x-6\right)$$

Rewrite the complete factored expression.

$$9x\left(x-6\right)$$

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.

$$9x^{2}-54x=0$$

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.

$$x=\frac{-\left(-54\right)±\sqrt{\left(-54\right)^{2}}}{2\times 9}$$

Take the square root of \left(-54\right)^{2}.

$$x=\frac{-\left(-54\right)±54}{2\times 9}$$

The opposite of -54 is 54.

$$x=\frac{54±54}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{54±54}{18}$$

Now solve the equation x=\frac{54±54}{18} when ± is plus. Add 54 to 54.

$$x=\frac{108}{18}$$

Divide 108 by 18.

$$x=6$$

Now solve the equation x=\frac{54±54}{18} when ± is minus. Subtract 54 from 54.

$$x=\frac{0}{18}$$

Divide 0 by 18.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 6 for x_{1} and 0 for x_{2}.

$$9x^{2}-54x=9\left(x-6\right)x$$

Evaluate

$$9x\left(x-6\right)$$