Solve 64+40x^2+72x

$$64 + 40 x ^ { 2 } + 72 x$$

Factor

$$8\left(5x^{2}+9x+8\right)$$

Solution Steps

Factor out 8. Polynomial 8+5x^{2}+9x is not factored since it does not have any rational roots.

$$8\left(8+5x^{2}+9x\right)$$

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.

$$40x^{2}+72x+64=0$$

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.

$$x=\frac{-72±\sqrt{72^{2}-4\times 40\times 64}}{2\times 40}$$

Square 72.

$$x=\frac{-72±\sqrt{5184-4\times 40\times 64}}{2\times 40}$$

Multiply -4 times 40.

$$x=\frac{-72±\sqrt{5184-160\times 64}}{2\times 40}$$

Multiply -160 times 64.

$$x=\frac{-72±\sqrt{5184-10240}}{2\times 40}$$

Add 5184 to -10240.

$$x=\frac{-72±\sqrt{-5056}}{2\times 40}$$

Since the square root of a negative number is not defined in the real field, there are no solutions. Quadratic polynomial cannot be factored.

$$40x^{2}+72x+64$$

Evaluate

$$40x^{2}+72x+64$$