Solve 100x^2-18x-25

$$100 { x }^{ 2 } -18x-25$$

Factor

$$100\left(x-\frac{9-\sqrt{2581}}{100}\right)\left(x-\frac{\sqrt{2581}+9}{100}\right)$$

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.

$$100x^{2}-18x-25=0$$

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.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 100\left(-25\right)}}{2\times 100}$$

Square -18.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\times 100\left(-25\right)}}{2\times 100}$$

Multiply -4 times 100.

$$x=\frac{-\left(-18\right)±\sqrt{324-400\left(-25\right)}}{2\times 100}$$

Multiply -400 times -25.

$$x=\frac{-\left(-18\right)±\sqrt{324+10000}}{2\times 100}$$

Add 324 to 10000.

$$x=\frac{-\left(-18\right)±\sqrt{10324}}{2\times 100}$$

Take the square root of 10324.

$$x=\frac{-\left(-18\right)±2\sqrt{2581}}{2\times 100}$$

The opposite of -18 is 18.

$$x=\frac{18±2\sqrt{2581}}{2\times 100}$$

Multiply 2 times 100.

$$x=\frac{18±2\sqrt{2581}}{200}$$

Now solve the equation x=\frac{18±2\sqrt{2581}}{200} when ± is plus. Add 18 to 2\sqrt{2581}.

$$x=\frac{2\sqrt{2581}+18}{200}$$

Divide 18+2\sqrt{2581} by 200.

$$x=\frac{\sqrt{2581}+9}{100}$$

Now solve the equation x=\frac{18±2\sqrt{2581}}{200} when ± is minus. Subtract 2\sqrt{2581} from 18.

$$x=\frac{18-2\sqrt{2581}}{200}$$

Divide 18-2\sqrt{2581} by 200.

$$x=\frac{9-\sqrt{2581}}{100}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{9+\sqrt{2581}}{100} for x_{1} and \frac{9-\sqrt{2581}}{100} for x_{2}.

$$100x^{2}-18x-25=100\left(x-\frac{\sqrt{2581}+9}{100}\right)\left(x-\frac{9-\sqrt{2581}}{100}\right)$$

Evaluate

$$100x^{2}-18x-25$$