Solve 4x+5-(4x*5x)=

$$4x+5-(4x \times 5x)=$$

Evaluate

$$5+4x-20x^{2}$$

Solution Steps

Multiply x and x to get x^{2}.

$$4x+5-4x^{2}\times 5$$

Multiply 4 and 5 to get 20.

$$4x+5-20x^{2}$$

Factor

$$-20\left(x-\frac{1-\sqrt{26}}{10}\right)\left(x-\frac{\sqrt{26}+1}{10}\right)$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$factor(4x+5-4x^{2}\times 5)$$

Multiply 4 and 5 to get 20.

$$factor(4x+5-20x^{2})$$

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.

$$-20x^{2}+4x+5=0$$

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.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-20\right)\times 5}}{2\left(-20\right)}$$

Square 4.

$$x=\frac{-4±\sqrt{16-4\left(-20\right)\times 5}}{2\left(-20\right)}$$

Multiply -4 times -20.

$$x=\frac{-4±\sqrt{16+80\times 5}}{2\left(-20\right)}$$

Multiply 80 times 5.

$$x=\frac{-4±\sqrt{16+400}}{2\left(-20\right)}$$

Add 16 to 400.

$$x=\frac{-4±\sqrt{416}}{2\left(-20\right)}$$

Take the square root of 416.

$$x=\frac{-4±4\sqrt{26}}{2\left(-20\right)}$$

Multiply 2 times -20.

$$x=\frac{-4±4\sqrt{26}}{-40}$$

Now solve the equation x=\frac{-4±4\sqrt{26}}{-40} when ± is plus. Add -4 to 4\sqrt{26}.

$$x=\frac{4\sqrt{26}-4}{-40}$$

Divide -4+4\sqrt{26} by -40.

$$x=\frac{1-\sqrt{26}}{10}$$

Now solve the equation x=\frac{-4±4\sqrt{26}}{-40} when ± is minus. Subtract 4\sqrt{26} from -4.

$$x=\frac{-4\sqrt{26}-4}{-40}$$

Divide -4-4\sqrt{26} by -40.

$$x=\frac{\sqrt{26}+1}{10}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{1-\sqrt{26}}{10} for x_{1} and \frac{1+\sqrt{26}}{10} for x_{2}.

$$-20x^{2}+4x+5=-20\left(x-\frac{1-\sqrt{26}}{10}\right)\left(x-\frac{\sqrt{26}+1}{10}\right)$$