# How do you solve a^2+a-30=0?

Jul 8, 2015

#### Answer:

Solve $y = {x}^{2} + x - 30 = 0$

#### Explanation:

$y = {x}^{2} + x - 30 = 0$
Find 2 numbers knowing sum (-1) and product (-30). Roots have opposite signs.
Factor pairs of (-30) --> ....(-3, 10)(-5, 6). This sum is 1 = b.
Then the 2 real roots are the opposite: $5 \mathmr{and} - 6$

Jul 8, 2015

#### Answer:

Factor the trinomial into two binomials. Set each binomial equal to zero and solve for $a$.

#### Explanation:

${a}^{2} + a - 30 = 0$

Find two numbers that when added equal $1$, and when multiplied equal $- 30$.

The numbers $- 5$ and $6$ fit the pattern.

${a}^{2} + a - 30 = 0$ =

$\left(a - 5\right) \left(a + 6\right) = 0$

Set $\left(a - 5\right)$ equal to zero and solve for $a$.

$a - 5 = 0$

$a = 5$

Set $\left(a + 6\right)$ equal to zero and solve for $a$.

$a + 6 = 0$

$a = - 6$

$a = - 6 , 5$