Solve {r}{4564x}{-7x^2}

$$\left. \begin{array} { r } { 4564 x } \\ { - 7 x ^ { 2 } } \end{array} \right.$$

Factor

$$7x\left(652-x\right)$$

Solution Steps

Factor out 7.

$$7\left(652x-x^{2}\right)$$

Consider 652x-x^{2}. Factor out x.

$$x\left(652-x\right)$$

Rewrite the complete factored expression.

$$7x\left(-x+652\right)$$

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.

$$-7x^{2}+4564x=0$$

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.

$$x=\frac{-4564±\sqrt{4564^{2}}}{2\left(-7\right)}$$

Take the square root of 4564^{2}.

$$x=\frac{-4564±4564}{2\left(-7\right)}$$

Multiply 2 times -7.

$$x=\frac{-4564±4564}{-14}$$

Now solve the equation x=\frac{-4564±4564}{-14} when ± is plus. Add -4564 to 4564.

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

Divide 0 by -14.

$$x=0$$

Now solve the equation x=\frac{-4564±4564}{-14} when ± is minus. Subtract 4564 from -4564.

$$x=-\frac{9128}{-14}$$

Divide -9128 by -14.

$$x=652$$

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 652 for x_{2}.

$$-7x^{2}+4564x=-7x\left(x-652\right)$$

Evaluate

$$7x\left(652-x\right)$$