Solve 16x^2+18x-774

$$16 { x }^{ 2 } +18x-774$$

Factor

$$16\left(x-\frac{-3\sqrt{1385}-9}{16}\right)\left(x-\frac{3\sqrt{1385}-9}{16}\right)$$

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.

$$16x^{2}+18x-774=0$$

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.

$$x=\frac{-18±\sqrt{18^{2}-4\times 16\left(-774\right)}}{2\times 16}$$

Square 18.

$$x=\frac{-18±\sqrt{324-4\times 16\left(-774\right)}}{2\times 16}$$

Multiply -4 times 16.

$$x=\frac{-18±\sqrt{324-64\left(-774\right)}}{2\times 16}$$

Multiply -64 times -774.

$$x=\frac{-18±\sqrt{324+49536}}{2\times 16}$$

Add 324 to 49536.

$$x=\frac{-18±\sqrt{49860}}{2\times 16}$$

Take the square root of 49860.

$$x=\frac{-18±6\sqrt{1385}}{2\times 16}$$

Multiply 2 times 16.

$$x=\frac{-18±6\sqrt{1385}}{32}$$

Now solve the equation x=\frac{-18±6\sqrt{1385}}{32} when ± is plus. Add -18 to 6\sqrt{1385}.

$$x=\frac{6\sqrt{1385}-18}{32}$$

Divide -18+6\sqrt{1385} by 32.

$$x=\frac{3\sqrt{1385}-9}{16}$$

Now solve the equation x=\frac{-18±6\sqrt{1385}}{32} when ± is minus. Subtract 6\sqrt{1385} from -18.

$$x=\frac{-6\sqrt{1385}-18}{32}$$

Divide -18-6\sqrt{1385} by 32.

$$x=\frac{-3\sqrt{1385}-9}{16}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-9+3\sqrt{1385}}{16} for x_{1} and \frac{-9-3\sqrt{1385}}{16} for x_{2}.

$$16x^{2}+18x-774=16\left(x-\frac{3\sqrt{1385}-9}{16}\right)\left(x-\frac{-3\sqrt{1385}-9}{16}\right)$$

Evaluate

$$16x^{2}+18x-774$$