Solve =4x-10+16-49x^2

$$= 4 x - 10 + 16 - 49 x ^ { 2 }$$

Factor

$$-49\left(x-\frac{2-\sqrt{298}}{49}\right)\left(x-\frac{\sqrt{298}+2}{49}\right)$$

Steps Using the Quadratic Formula

Add -10 and 16 to get 6.

$$factor(4x+6-49x^{2})$$

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.

$$-49x^{2}+4x+6=0$$

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.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-49\right)\times 6}}{2\left(-49\right)}$$

Square 4.

$$x=\frac{-4±\sqrt{16-4\left(-49\right)\times 6}}{2\left(-49\right)}$$

Multiply -4 times -49.

$$x=\frac{-4±\sqrt{16+196\times 6}}{2\left(-49\right)}$$

Multiply 196 times 6.

$$x=\frac{-4±\sqrt{16+1176}}{2\left(-49\right)}$$

Add 16 to 1176.

$$x=\frac{-4±\sqrt{1192}}{2\left(-49\right)}$$

Take the square root of 1192.

$$x=\frac{-4±2\sqrt{298}}{2\left(-49\right)}$$

Multiply 2 times -49.

$$x=\frac{-4±2\sqrt{298}}{-98}$$

Now solve the equation x=\frac{-4±2\sqrt{298}}{-98} when ± is plus. Add -4 to 2\sqrt{298}.

$$x=\frac{2\sqrt{298}-4}{-98}$$

Divide -4+2\sqrt{298} by -98.

$$x=\frac{2-\sqrt{298}}{49}$$

Now solve the equation x=\frac{-4±2\sqrt{298}}{-98} when ± is minus. Subtract 2\sqrt{298} from -4.

$$x=\frac{-2\sqrt{298}-4}{-98}$$

Divide -4-2\sqrt{298} by -98.

$$x=\frac{\sqrt{298}+2}{49}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{2-\sqrt{298}}{49} for x_{1} and \frac{2+\sqrt{298}}{49} for x_{2}.

$$-49x^{2}+4x+6=-49\left(x-\frac{2-\sqrt{298}}{49}\right)\left(x-\frac{\sqrt{298}+2}{49}\right)$$

Evaluate

$$6+4x-49x^{2}$$

Solution Steps

Add -10 and 16 to get 6.

$$4x+6-49x^{2}$$