Solve 7+49a^2-14a

$$7 + 49 a ^ { 2 } - 14 a$$

Factor

$$7\left(7a^{2}-2a+1\right)$$

Solution Steps

Factor out 7. Polynomial 1+7a^{2}-2a is not factored since it does not have any rational roots.

$$7\left(1+7a^{2}-2a\right)$$

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.

$$49a^{2}-14a+7=0$$

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.

$$a=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 49\times 7}}{2\times 49}$$

Square -14.

$$a=\frac{-\left(-14\right)±\sqrt{196-4\times 49\times 7}}{2\times 49}$$

Multiply -4 times 49.

$$a=\frac{-\left(-14\right)±\sqrt{196-196\times 7}}{2\times 49}$$

Multiply -196 times 7.

$$a=\frac{-\left(-14\right)±\sqrt{196-1372}}{2\times 49}$$

Add 196 to -1372.

$$a=\frac{-\left(-14\right)±\sqrt{-1176}}{2\times 49}$$

Since the square root of a negative number is not defined in the real field, there are no solutions. Quadratic polynomial cannot be factored.

$$49a^{2}-14a+7$$

Evaluate

$$49a^{2}-14a+7$$