Solve 360x-45x^2

$$360 x - 45 x ^ { 2 }$$

Factor

$$45x\left(8-x\right)$$

Solution Steps

Factor out 45.

$$45\left(8x-x^{2}\right)$$

Consider 8x-x^{2}. Factor out x.

$$x\left(8-x\right)$$

Rewrite the complete factored expression.

$$45x\left(-x+8\right)$$

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.

$$-45x^{2}+360x=0$$

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.

$$x=\frac{-360±\sqrt{360^{2}}}{2\left(-45\right)}$$

Take the square root of 360^{2}.

$$x=\frac{-360±360}{2\left(-45\right)}$$

Multiply 2 times -45.

$$x=\frac{-360±360}{-90}$$

Now solve the equation x=\frac{-360±360}{-90} when ± is plus. Add -360 to 360.

$$x=\frac{0}{-90}$$

Divide 0 by -90.

$$x=0$$

Now solve the equation x=\frac{-360±360}{-90} when ± is minus. Subtract 360 from -360.

$$x=-\frac{720}{-90}$$

Divide -720 by -90.

$$x=8$$

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 8 for x_{2}.

$$-45x^{2}+360x=-45x\left(x-8\right)$$

Evaluate

$$45x\left(8-x\right)$$