Solve 26+x-12x^2

$$26 + x - 12 x ^ { 2 }$$

Factor

$$-12\left(x-\frac{1-\sqrt{1249}}{24}\right)\left(x-\frac{\sqrt{1249}+1}{24}\right)$$

Steps Using the Quadratic Formula

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.

$$-12x^{2}+x+26=0$$

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.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-12\right)\times 26}}{2\left(-12\right)}$$

Square 1.

$$x=\frac{-1±\sqrt{1-4\left(-12\right)\times 26}}{2\left(-12\right)}$$

Multiply -4 times -12.

$$x=\frac{-1±\sqrt{1+48\times 26}}{2\left(-12\right)}$$

Multiply 48 times 26.

$$x=\frac{-1±\sqrt{1+1248}}{2\left(-12\right)}$$

Add 1 to 1248.

$$x=\frac{-1±\sqrt{1249}}{2\left(-12\right)}$$

Multiply 2 times -12.

$$x=\frac{-1±\sqrt{1249}}{-24}$$

Now solve the equation x=\frac{-1±\sqrt{1249}}{-24} when ± is plus. Add -1 to \sqrt{1249}.

$$x=\frac{\sqrt{1249}-1}{-24}$$

Divide -1+\sqrt{1249} by -24.

$$x=\frac{1-\sqrt{1249}}{24}$$

Now solve the equation x=\frac{-1±\sqrt{1249}}{-24} when ± is minus. Subtract \sqrt{1249} from -1.

$$x=\frac{-\sqrt{1249}-1}{-24}$$

Divide -1-\sqrt{1249} by -24.

$$x=\frac{\sqrt{1249}+1}{24}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{1-\sqrt{1249}}{24} for x_{1} and \frac{1+\sqrt{1249}}{24} for x_{2}.

$$-12x^{2}+x+26=-12\left(x-\frac{1-\sqrt{1249}}{24}\right)\left(x-\frac{\sqrt{1249}+1}{24}\right)$$

Evaluate

$$26+x-12x^{2}$$