# How do you solve a^2-2a-224=0?

Jul 8, 2015

Solve $y = {x}^{2} - 2 x - 224 = 0$

#### Explanation:

$y = {x}^{2} - 2 x - 224 = 0$.
I use the new Transforming Method (Google Yahoo Search)
Find 2 numbers knowing sum (2) and product (-224). Roots have different signs.
Factor pairs of (-224) -> ...(-8, 28)(-14, 16). This sum is 2 = -b. Then, the 2 real roots are: $- 14 \mathmr{and} 16.$

Jul 8, 2015

Factor the trinomial as the product of two binomials. Set each binomial equal to zero, and solve for $a$.

#### Explanation:

${a}^{2} - 2 a - 224 = 0$

Find two numbers that when added equal $- 2$, and when multiplied equal $- 224$. The numbers $- 16$ and $14$ fit the pattern.

${a}^{2} - 2 a - 224 = 0$ =

$\left(a - 16\right) \left(a + 14\right) = 0$

Set $\left(a - 16\right)$ equal to zero and solve for $a$.

$a - 16 = 0$

#a=16

Set $\left(a + 14\right)$ equal to zero and solve for $a$.

$a + 14 = 0$

$a = - 14$

$a = 16 , - 14$