Solve k^2-2*72k-10

$$k ^ { 2 } - 2 \cdot 72 k - 10$$

Factor

$$\left(k-\left(72-7\sqrt{106}\right)\right)\left(k-\left(7\sqrt{106}+72\right)\right)$$

Steps Using the Quadratic Formula

Multiply 2 and 72 to get 144.

$$factor(k^{2}-144k-10)$$

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.

$$k^{2}-144k-10=0$$

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.

$$k=\frac{-\left(-144\right)±\sqrt{\left(-144\right)^{2}-4\left(-10\right)}}{2}$$

Square -144.

$$k=\frac{-\left(-144\right)±\sqrt{20736-4\left(-10\right)}}{2}$$

Multiply -4 times -10.

$$k=\frac{-\left(-144\right)±\sqrt{20736+40}}{2}$$

Add 20736 to 40.

$$k=\frac{-\left(-144\right)±\sqrt{20776}}{2}$$

Take the square root of 20776.

$$k=\frac{-\left(-144\right)±14\sqrt{106}}{2}$$

The opposite of -144 is 144.

$$k=\frac{144±14\sqrt{106}}{2}$$

Now solve the equation k=\frac{144±14\sqrt{106}}{2} when ± is plus. Add 144 to 14\sqrt{106}.

$$k=\frac{14\sqrt{106}+144}{2}$$

Divide 144+14\sqrt{106} by 2.

$$k=7\sqrt{106}+72$$

Now solve the equation k=\frac{144±14\sqrt{106}}{2} when ± is minus. Subtract 14\sqrt{106} from 144.

$$k=\frac{144-14\sqrt{106}}{2}$$

Divide 144-14\sqrt{106} by 2.

$$k=72-7\sqrt{106}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 72+7\sqrt{106} for x_{1} and 72-7\sqrt{106} for x_{2}.

$$k^{2}-144k-10=\left(k-\left(7\sqrt{106}+72\right)\right)\left(k-\left(72-7\sqrt{106}\right)\right)$$

Evaluate

$$k^{2}-144k-10$$

Solution Steps

Multiply 2 and 72 to get 144.

$$k^{2}-144k-10$$