Solve -5x^2+6x+55

$$-5 { x }^{ 2 } +6x+55$$

Factor

$$-5\left(x-\frac{3-2\sqrt{71}}{5}\right)\left(x-\frac{2\sqrt{71}+3}{5}\right)$$

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.

$$-5x^{2}+6x+55=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\left(-5\right)\times 55}}{2\left(-5\right)}$$

Square 6.

$$x=\frac{-6±\sqrt{36-4\left(-5\right)\times 55}}{2\left(-5\right)}$$

Multiply -4 times -5.

$$x=\frac{-6±\sqrt{36+20\times 55}}{2\left(-5\right)}$$

Multiply 20 times 55.

$$x=\frac{-6±\sqrt{36+1100}}{2\left(-5\right)}$$

Add 36 to 1100.

$$x=\frac{-6±\sqrt{1136}}{2\left(-5\right)}$$

Take the square root of 1136.

$$x=\frac{-6±4\sqrt{71}}{2\left(-5\right)}$$

Multiply 2 times -5.

$$x=\frac{-6±4\sqrt{71}}{-10}$$

Now solve the equation x=\frac{-6±4\sqrt{71}}{-10} when ± is plus. Add -6 to 4\sqrt{71}.

$$x=\frac{4\sqrt{71}-6}{-10}$$

Divide -6+4\sqrt{71} by -10.

$$x=\frac{3-2\sqrt{71}}{5}$$

Now solve the equation x=\frac{-6±4\sqrt{71}}{-10} when ± is minus. Subtract 4\sqrt{71} from -6.

$$x=\frac{-4\sqrt{71}-6}{-10}$$

Divide -6-4\sqrt{71} by -10.

$$x=\frac{2\sqrt{71}+3}{5}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{3-2\sqrt{71}}{5} for x_{1} and \frac{3+2\sqrt{71}}{5} for x_{2}.

$$-5x^{2}+6x+55=-5\left(x-\frac{3-2\sqrt{71}}{5}\right)\left(x-\frac{2\sqrt{71}+3}{5}\right)$$

Evaluate

$$55+6x-5x^{2}$$