Solve x^2+49x+58+x+6

$${ x }^{ 2 } +49x+58+x+6$$

Evaluate

$$x^{2}+50x+64$$

Solution Steps

Combine 49x and x to get 50x.

$$x^{2}+50x+58+6$$

Add 58 and 6 to get 64.

$$x^{2}+50x+64$$

Factor

$$\left(x-\left(-\sqrt{561}-25\right)\right)\left(x-\left(\sqrt{561}-25\right)\right)$$

Steps Using the Quadratic Formula

Combine 49x and x to get 50x.

$$factor(x^{2}+50x+58+6)$$

Add 58 and 6 to get 64.

$$factor(x^{2}+50x+64)$$

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.

$$x^{2}+50x+64=0$$

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.

$$x=\frac{-50±\sqrt{50^{2}-4\times 64}}{2}$$

Square 50.

$$x=\frac{-50±\sqrt{2500-4\times 64}}{2}$$

Multiply -4 times 64.

$$x=\frac{-50±\sqrt{2500-256}}{2}$$

Add 2500 to -256.

$$x=\frac{-50±\sqrt{2244}}{2}$$

Take the square root of 2244.

$$x=\frac{-50±2\sqrt{561}}{2}$$

Now solve the equation x=\frac{-50±2\sqrt{561}}{2} when ± is plus. Add -50 to 2\sqrt{561}.

$$x=\frac{2\sqrt{561}-50}{2}$$

Divide -50+2\sqrt{561} by 2.

$$x=\sqrt{561}-25$$

Now solve the equation x=\frac{-50±2\sqrt{561}}{2} when ± is minus. Subtract 2\sqrt{561} from -50.

$$x=\frac{-2\sqrt{561}-50}{2}$$

Divide -50-2\sqrt{561} by 2.

$$x=-\sqrt{561}-25$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -25+\sqrt{561} for x_{1} and -25-\sqrt{561} for x_{2}.

$$x^{2}+50x+64=\left(x-\left(\sqrt{561}-25\right)\right)\left(x-\left(-\sqrt{561}-25\right)\right)$$