Solve 0*3x^2-5x+431-x^2

$$0 \cdot 3 x ^ { 2 } - 5 x + 431 - x ^ { 2 }$$

Evaluate

$$431-5x-x^{2}$$

Solution Steps

Multiply 0 and 3 to get 0.

$$0x^{2}-5x+431-x^{2}$$

Anything times zero gives zero.

$$0-5x+431-x^{2}$$

Add 0 and 431 to get 431.

$$431-5x-x^{2}$$

Factor

$$-\left(x-\frac{-\sqrt{1749}-5}{2}\right)\left(x-\frac{\sqrt{1749}-5}{2}\right)$$

Steps Using the Quadratic Formula

Multiply 0 and 3 to get 0.

$$factor(0x^{2}-5x+431-x^{2})$$

Anything times zero gives zero.

$$factor(0-5x+431-x^{2})$$

Add 0 and 431 to get 431.

$$factor(431-5x-x^{2})$$

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.

$$-x^{2}-5x+431=0$$

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.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\left(-1\right)\times 431}}{2\left(-1\right)}$$

Square -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\left(-1\right)\times 431}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{-\left(-5\right)±\sqrt{25+4\times 431}}{2\left(-1\right)}$$

Multiply 4 times 431.

$$x=\frac{-\left(-5\right)±\sqrt{25+1724}}{2\left(-1\right)}$$

Add 25 to 1724.

$$x=\frac{-\left(-5\right)±\sqrt{1749}}{2\left(-1\right)}$$

The opposite of -5 is 5.

$$x=\frac{5±\sqrt{1749}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{5±\sqrt{1749}}{-2}$$

Now solve the equation x=\frac{5±\sqrt{1749}}{-2} when ± is plus. Add 5 to \sqrt{1749}.

$$x=\frac{\sqrt{1749}+5}{-2}$$

Divide 5+\sqrt{1749} by -2.

$$x=\frac{-\sqrt{1749}-5}{2}$$

Now solve the equation x=\frac{5±\sqrt{1749}}{-2} when ± is minus. Subtract \sqrt{1749} from 5.

$$x=\frac{5-\sqrt{1749}}{-2}$$

Divide 5-\sqrt{1749} by -2.

$$x=\frac{\sqrt{1749}-5}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-5-\sqrt{1749}}{2} for x_{1} and \frac{-5+\sqrt{1749}}{2} for x_{2}.

$$-x^{2}-5x+431=-\left(x-\frac{-\sqrt{1749}-5}{2}\right)\left(x-\frac{\sqrt{1749}-5}{2}\right)$$