Solve 49x^2+2x-15

$$49 { x }^{ 2 } +2x-15$$

Factor

$$49\left(x-\frac{-4\sqrt{46}-1}{49}\right)\left(x-\frac{4\sqrt{46}-1}{49}\right)$$

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.

$$49x^{2}+2x-15=0$$

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.

$$x=\frac{-2±\sqrt{2^{2}-4\times 49\left(-15\right)}}{2\times 49}$$

Square 2.

$$x=\frac{-2±\sqrt{4-4\times 49\left(-15\right)}}{2\times 49}$$

Multiply -4 times 49.

$$x=\frac{-2±\sqrt{4-196\left(-15\right)}}{2\times 49}$$

Multiply -196 times -15.

$$x=\frac{-2±\sqrt{4+2940}}{2\times 49}$$

Add 4 to 2940.

$$x=\frac{-2±\sqrt{2944}}{2\times 49}$$

Take the square root of 2944.

$$x=\frac{-2±8\sqrt{46}}{2\times 49}$$

Multiply 2 times 49.

$$x=\frac{-2±8\sqrt{46}}{98}$$

Now solve the equation x=\frac{-2±8\sqrt{46}}{98} when ± is plus. Add -2 to 8\sqrt{46}.

$$x=\frac{8\sqrt{46}-2}{98}$$

Divide -2+8\sqrt{46} by 98.

$$x=\frac{4\sqrt{46}-1}{49}$$

Now solve the equation x=\frac{-2±8\sqrt{46}}{98} when ± is minus. Subtract 8\sqrt{46} from -2.

$$x=\frac{-8\sqrt{46}-2}{98}$$

Divide -2-8\sqrt{46} by 98.

$$x=\frac{-4\sqrt{46}-1}{49}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-1+4\sqrt{46}}{49} for x_{1} and \frac{-1-4\sqrt{46}}{49} for x_{2}.

$$49x^{2}+2x-15=49\left(x-\frac{4\sqrt{46}-1}{49}\right)\left(x-\frac{-4\sqrt{46}-1}{49}\right)$$

Evaluate

$$49x^{2}+2x-15$$