Solve 2-2-5x+3-3x^2

$$2 - 2 - 5 x + 3 - 3 x ^ { 2 }$$

Factor

$$-3\left(x-\frac{-\sqrt{61}-5}{6}\right)\left(x-\frac{\sqrt{61}-5}{6}\right)$$

Steps Using the Quadratic Formula

Subtract 2 from 2 to get 0.

$$factor(-5x+3-3x^{2})$$

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.

$$-3x^{2}-5x+3=0$$

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.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\left(-3\right)\times 3}}{2\left(-3\right)}$$

Square -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\left(-3\right)\times 3}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{-\left(-5\right)±\sqrt{25+12\times 3}}{2\left(-3\right)}$$

Multiply 12 times 3.

$$x=\frac{-\left(-5\right)±\sqrt{25+36}}{2\left(-3\right)}$$

Add 25 to 36.

$$x=\frac{-\left(-5\right)±\sqrt{61}}{2\left(-3\right)}$$

The opposite of -5 is 5.

$$x=\frac{5±\sqrt{61}}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{5±\sqrt{61}}{-6}$$

Now solve the equation x=\frac{5±\sqrt{61}}{-6} when ± is plus. Add 5 to \sqrt{61}.

$$x=\frac{\sqrt{61}+5}{-6}$$

Divide 5+\sqrt{61} by -6.

$$x=\frac{-\sqrt{61}-5}{6}$$

Now solve the equation x=\frac{5±\sqrt{61}}{-6} when ± is minus. Subtract \sqrt{61} from 5.

$$x=\frac{5-\sqrt{61}}{-6}$$

Divide 5-\sqrt{61} by -6.

$$x=\frac{\sqrt{61}-5}{6}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-5-\sqrt{61}}{6} for x_{1} and \frac{-5+\sqrt{61}}{6} for x_{2}.

$$-3x^{2}-5x+3=-3\left(x-\frac{-\sqrt{61}-5}{6}\right)\left(x-\frac{\sqrt{61}-5}{6}\right)$$

Evaluate

$$3-5x-3x^{2}$$

Solution Steps

Subtract 2 from 2 to get 0.

$$-5x+3-3x^{2}$$