Solve x^2+9261x-343^2

$${ x }^{ 2 } +9261x- { 343 }^{ 2 }$$

Factor

$$\left(x-\frac{-343\sqrt{733}-9261}{2}\right)\left(x-\frac{343\sqrt{733}-9261}{2}\right)$$

Steps Using the Quadratic Formula

Calculate 343 to the power of 2 and get 117649.

$$factor(x^{2}+9261x-117649)$$

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.

$$x^{2}+9261x-117649=0$$

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.

$$x=\frac{-9261±\sqrt{9261^{2}-4\left(-117649\right)}}{2}$$

Square 9261.

$$x=\frac{-9261±\sqrt{85766121-4\left(-117649\right)}}{2}$$

Multiply -4 times -117649.

$$x=\frac{-9261±\sqrt{85766121+470596}}{2}$$

Add 85766121 to 470596.

$$x=\frac{-9261±\sqrt{86236717}}{2}$$

Take the square root of 86236717.

$$x=\frac{-9261±343\sqrt{733}}{2}$$

Now solve the equation x=\frac{-9261±343\sqrt{733}}{2} when ± is plus. Add -9261 to 343\sqrt{733}.

$$x=\frac{343\sqrt{733}-9261}{2}$$

Now solve the equation x=\frac{-9261±343\sqrt{733}}{2} when ± is minus. Subtract 343\sqrt{733} from -9261.

$$x=\frac{-343\sqrt{733}-9261}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-9261+343\sqrt{733}}{2} for x_{1} and \frac{-9261-343\sqrt{733}}{2} for x_{2}.

$$x^{2}+9261x-117649=\left(x-\frac{343\sqrt{733}-9261}{2}\right)\left(x-\frac{-343\sqrt{733}-9261}{2}\right)$$

Evaluate

$$x^{2}+9261x-117649$$

Solution Steps

Calculate 343 to the power of 2 and get 117649.

$$x^{2}+9261x-117649$$