Solve 5x^2+238-70x

$$5 x ^ { 2 } + 238 - 70 x$$

Factor

$$5\left(x-\left(-\frac{\sqrt{35}}{5}+7\right)\right)\left(x-\left(\frac{\sqrt{35}}{5}+7\right)\right)$$

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.

$$5x^{2}-70x+238=0$$

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.

$$x=\frac{-\left(-70\right)±\sqrt{\left(-70\right)^{2}-4\times 5\times 238}}{2\times 5}$$

Square -70.

$$x=\frac{-\left(-70\right)±\sqrt{4900-4\times 5\times 238}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{-\left(-70\right)±\sqrt{4900-20\times 238}}{2\times 5}$$

Multiply -20 times 238.

$$x=\frac{-\left(-70\right)±\sqrt{4900-4760}}{2\times 5}$$

Add 4900 to -4760.

$$x=\frac{-\left(-70\right)±\sqrt{140}}{2\times 5}$$

Take the square root of 140.

$$x=\frac{-\left(-70\right)±2\sqrt{35}}{2\times 5}$$

The opposite of -70 is 70.

$$x=\frac{70±2\sqrt{35}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{70±2\sqrt{35}}{10}$$

Now solve the equation x=\frac{70±2\sqrt{35}}{10} when ± is plus. Add 70 to 2\sqrt{35}.

$$x=\frac{2\sqrt{35}+70}{10}$$

Divide 70+2\sqrt{35} by 10.

$$x=\frac{\sqrt{35}}{5}+7$$

Now solve the equation x=\frac{70±2\sqrt{35}}{10} when ± is minus. Subtract 2\sqrt{35} from 70.

$$x=\frac{70-2\sqrt{35}}{10}$$

Divide 70-2\sqrt{35} by 10.

$$x=-\frac{\sqrt{35}}{5}+7$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 7+\frac{\sqrt{35}}{5} for x_{1} and 7-\frac{\sqrt{35}}{5} for x_{2}.

$$5x^{2}-70x+238=5\left(x-\left(\frac{\sqrt{35}}{5}+7\right)\right)\left(x-\left(-\frac{\sqrt{35}}{5}+7\right)\right)$$

Evaluate

$$5x^{2}-70x+238$$