Solve 10x^2-80x+151

$$10 { x }^{ 2 } -80x+151$$

Factor

$$10\left(x-\left(-\frac{3\sqrt{10}}{10}+4\right)\right)\left(x-\left(\frac{3\sqrt{10}}{10}+4\right)\right)$$

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.

$$10x^{2}-80x+151=0$$

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.

$$x=\frac{-\left(-80\right)±\sqrt{\left(-80\right)^{2}-4\times 10\times 151}}{2\times 10}$$

Square -80.

$$x=\frac{-\left(-80\right)±\sqrt{6400-4\times 10\times 151}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{-\left(-80\right)±\sqrt{6400-40\times 151}}{2\times 10}$$

Multiply -40 times 151.

$$x=\frac{-\left(-80\right)±\sqrt{6400-6040}}{2\times 10}$$

Add 6400 to -6040.

$$x=\frac{-\left(-80\right)±\sqrt{360}}{2\times 10}$$

Take the square root of 360.

$$x=\frac{-\left(-80\right)±6\sqrt{10}}{2\times 10}$$

The opposite of -80 is 80.

$$x=\frac{80±6\sqrt{10}}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{80±6\sqrt{10}}{20}$$

Now solve the equation x=\frac{80±6\sqrt{10}}{20} when ± is plus. Add 80 to 6\sqrt{10}.

$$x=\frac{6\sqrt{10}+80}{20}$$

Divide 80+6\sqrt{10} by 20.

$$x=\frac{3\sqrt{10}}{10}+4$$

Now solve the equation x=\frac{80±6\sqrt{10}}{20} when ± is minus. Subtract 6\sqrt{10} from 80.

$$x=\frac{80-6\sqrt{10}}{20}$$

Divide 80-6\sqrt{10} by 20.

$$x=-\frac{3\sqrt{10}}{10}+4$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 4+\frac{3\sqrt{10}}{10} for x_{1} and 4-\frac{3\sqrt{10}}{10} for x_{2}.

$$10x^{2}-80x+151=10\left(x-\left(\frac{3\sqrt{10}}{10}+4\right)\right)\left(x-\left(-\frac{3\sqrt{10}}{10}+4\right)\right)$$

Evaluate

$$10x^{2}-80x+151$$