Solve (-8x-1)+(7x^2+3x)

$$( - 8 x - 1 ) + ( 7 x ^ { 2 } + 3 x )$$

Factor

$$7\left(x-\frac{5-\sqrt{53}}{14}\right)\left(x-\frac{\sqrt{53}+5}{14}\right)$$

Steps Using the Quadratic Formula

Combine -8x and 3x to get -5x.

$$factor(-5x-1+7x^{2})$$

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.

$$7x^{2}-5x-1=0$$

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.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 7\left(-1\right)}}{2\times 7}$$

Square -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 7\left(-1\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{-\left(-5\right)±\sqrt{25-28\left(-1\right)}}{2\times 7}$$

Multiply -28 times -1.

$$x=\frac{-\left(-5\right)±\sqrt{25+28}}{2\times 7}$$

Add 25 to 28.

$$x=\frac{-\left(-5\right)±\sqrt{53}}{2\times 7}$$

The opposite of -5 is 5.

$$x=\frac{5±\sqrt{53}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{5±\sqrt{53}}{14}$$

Now solve the equation x=\frac{5±\sqrt{53}}{14} when ± is plus. Add 5 to \sqrt{53}.

$$x=\frac{\sqrt{53}+5}{14}$$

Now solve the equation x=\frac{5±\sqrt{53}}{14} when ± is minus. Subtract \sqrt{53} from 5.

$$x=\frac{5-\sqrt{53}}{14}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{5+\sqrt{53}}{14} for x_{1} and \frac{5-\sqrt{53}}{14} for x_{2}.

$$7x^{2}-5x-1=7\left(x-\frac{\sqrt{53}+5}{14}\right)\left(x-\frac{5-\sqrt{53}}{14}\right)$$

Evaluate

$$7x^{2}-5x-1$$

Solution Steps

Combine -8x and 3x to get -5x.

$$-5x-1+7x^{2}$$