Solve a-27+5a^2

$$a - 27 + 5 a ^ { 2 }$$

Factor

$$5\left(a-\frac{-\sqrt{541}-1}{10}\right)\left(a-\frac{\sqrt{541}-1}{10}\right)$$

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.

$$5a^{2}+a-27=0$$

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.

$$a=\frac{-1±\sqrt{1^{2}-4\times 5\left(-27\right)}}{2\times 5}$$

Square 1.

$$a=\frac{-1±\sqrt{1-4\times 5\left(-27\right)}}{2\times 5}$$

Multiply -4 times 5.

$$a=\frac{-1±\sqrt{1-20\left(-27\right)}}{2\times 5}$$

Multiply -20 times -27.

$$a=\frac{-1±\sqrt{1+540}}{2\times 5}$$

Add 1 to 540.

$$a=\frac{-1±\sqrt{541}}{2\times 5}$$

Multiply 2 times 5.

$$a=\frac{-1±\sqrt{541}}{10}$$

Now solve the equation a=\frac{-1±\sqrt{541}}{10} when ± is plus. Add -1 to \sqrt{541}.

$$a=\frac{\sqrt{541}-1}{10}$$

Now solve the equation a=\frac{-1±\sqrt{541}}{10} when ± is minus. Subtract \sqrt{541} from -1.

$$a=\frac{-\sqrt{541}-1}{10}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-1+\sqrt{541}}{10} for x_{1} and \frac{-1-\sqrt{541}}{10} for x_{2}.

$$5a^{2}+a-27=5\left(a-\frac{\sqrt{541}-1}{10}\right)\left(a-\frac{-\sqrt{541}-1}{10}\right)$$

Evaluate

$$5a^{2}+a-27$$