Solve 680000+1300a^2+800a

$$680000 + 1300 a ^ { 2 } + 800 a$$

Factor

$$100\left(13a^{2}+8a+6800\right)$$

Solution Steps

Factor out 100. Polynomial 6800+13a^{2}+8a is not factored since it does not have any rational roots.

$$100\left(6800+13a^{2}+8a\right)$$

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.

$$1300a^{2}+800a+680000=0$$

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.

$$a=\frac{-800±\sqrt{800^{2}-4\times 1300\times 680000}}{2\times 1300}$$

Square 800.

$$a=\frac{-800±\sqrt{640000-4\times 1300\times 680000}}{2\times 1300}$$

Multiply -4 times 1300.

$$a=\frac{-800±\sqrt{640000-5200\times 680000}}{2\times 1300}$$

Multiply -5200 times 680000.

$$a=\frac{-800±\sqrt{640000-3536000000}}{2\times 1300}$$

Add 640000 to -3536000000.

$$a=\frac{-800±\sqrt{-3535360000}}{2\times 1300}$$

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

$$1300a^{2}+800a+680000$$

Evaluate

$$1300a^{2}+800a+680000$$