Solve 7x+10x^2-144

$$7 x + 10 x ^ { 2 } - 144$$

Factor

$$10\left(x-\frac{-\sqrt{5809}-7}{20}\right)\left(x-\frac{\sqrt{5809}-7}{20}\right)$$

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.

$$10x^{2}+7x-144=0$$

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.

$$x=\frac{-7±\sqrt{7^{2}-4\times 10\left(-144\right)}}{2\times 10}$$

Square 7.

$$x=\frac{-7±\sqrt{49-4\times 10\left(-144\right)}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{-7±\sqrt{49-40\left(-144\right)}}{2\times 10}$$

Multiply -40 times -144.

$$x=\frac{-7±\sqrt{49+5760}}{2\times 10}$$

Add 49 to 5760.

$$x=\frac{-7±\sqrt{5809}}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{-7±\sqrt{5809}}{20}$$

Now solve the equation x=\frac{-7±\sqrt{5809}}{20} when ± is plus. Add -7 to \sqrt{5809}.

$$x=\frac{\sqrt{5809}-7}{20}$$

Now solve the equation x=\frac{-7±\sqrt{5809}}{20} when ± is minus. Subtract \sqrt{5809} from -7.

$$x=\frac{-\sqrt{5809}-7}{20}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-7+\sqrt{5809}}{20} for x_{1} and \frac{-7-\sqrt{5809}}{20} for x_{2}.

$$10x^{2}+7x-144=10\left(x-\frac{\sqrt{5809}-7}{20}\right)\left(x-\frac{-\sqrt{5809}-7}{20}\right)$$

Evaluate

$$10x^{2}+7x-144$$