Solve 300x+20-5x+10-40x^2=

$$300 x + 20 - 5 x + 10 - 40 x ^ { 2 } =$$

Evaluate

$$30+295x-40x^{2}$$

Solution Steps

Combine 300x and -5x to get 295x.

$$295x+20+10-40x^{2}$$

Add 20 and 10 to get 30.

$$295x+30-40x^{2}$$

Factor

$$-40\left(x-\frac{59-\sqrt{3673}}{16}\right)\left(x-\frac{\sqrt{3673}+59}{16}\right)$$

Steps Using the Quadratic Formula

Combine 300x and -5x to get 295x.

$$factor(295x+20+10-40x^{2})$$

Add 20 and 10 to get 30.

$$factor(295x+30-40x^{2})$$

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.

$$-40x^{2}+295x+30=0$$

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.

$$x=\frac{-295±\sqrt{295^{2}-4\left(-40\right)\times 30}}{2\left(-40\right)}$$

Square 295.

$$x=\frac{-295±\sqrt{87025-4\left(-40\right)\times 30}}{2\left(-40\right)}$$

Multiply -4 times -40.

$$x=\frac{-295±\sqrt{87025+160\times 30}}{2\left(-40\right)}$$

Multiply 160 times 30.

$$x=\frac{-295±\sqrt{87025+4800}}{2\left(-40\right)}$$

Add 87025 to 4800.

$$x=\frac{-295±\sqrt{91825}}{2\left(-40\right)}$$

Take the square root of 91825.

$$x=\frac{-295±5\sqrt{3673}}{2\left(-40\right)}$$

Multiply 2 times -40.

$$x=\frac{-295±5\sqrt{3673}}{-80}$$

Now solve the equation x=\frac{-295±5\sqrt{3673}}{-80} when ± is plus. Add -295 to 5\sqrt{3673}.

$$x=\frac{5\sqrt{3673}-295}{-80}$$

Divide -295+5\sqrt{3673} by -80.

$$x=\frac{59-\sqrt{3673}}{16}$$

Now solve the equation x=\frac{-295±5\sqrt{3673}}{-80} when ± is minus. Subtract 5\sqrt{3673} from -295.

$$x=\frac{-5\sqrt{3673}-295}{-80}$$

Divide -295-5\sqrt{3673} by -80.

$$x=\frac{\sqrt{3673}+59}{16}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{59-\sqrt{3673}}{16} for x_{1} and \frac{59+\sqrt{3673}}{16} for x_{2}.

$$-40x^{2}+295x+30=-40\left(x-\frac{59-\sqrt{3673}}{16}\right)\left(x-\frac{\sqrt{3673}+59}{16}\right)$$