Solve 5-s^2+6s

$$5 - s ^ { 2 } + 6 s$$

Factor

$$-\left(s-\left(3-\sqrt{14}\right)\right)\left(s-\left(\sqrt{14}+3\right)\right)$$

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.

$$-s^{2}+6s+5=0$$

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.

$$s=\frac{-6±\sqrt{6^{2}-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

Square 6.

$$s=\frac{-6±\sqrt{36-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$s=\frac{-6±\sqrt{36+4\times 5}}{2\left(-1\right)}$$

Multiply 4 times 5.

$$s=\frac{-6±\sqrt{36+20}}{2\left(-1\right)}$$

Add 36 to 20.

$$s=\frac{-6±\sqrt{56}}{2\left(-1\right)}$$

Take the square root of 56.

$$s=\frac{-6±2\sqrt{14}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$s=\frac{-6±2\sqrt{14}}{-2}$$

Now solve the equation s=\frac{-6±2\sqrt{14}}{-2} when ± is plus. Add -6 to 2\sqrt{14}.

$$s=\frac{2\sqrt{14}-6}{-2}$$

Divide -6+2\sqrt{14} by -2.

$$s=3-\sqrt{14}$$

Now solve the equation s=\frac{-6±2\sqrt{14}}{-2} when ± is minus. Subtract 2\sqrt{14} from -6.

$$s=\frac{-2\sqrt{14}-6}{-2}$$

Divide -6-2\sqrt{14} by -2.

$$s=\sqrt{14}+3$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 3-\sqrt{14} for x_{1} and 3+\sqrt{14} for x_{2}.

$$-s^{2}+6s+5=-\left(s-\left(3-\sqrt{14}\right)\right)\left(s-\left(\sqrt{14}+3\right)\right)$$

Evaluate

$$5+6s-s^{2}$$