Question

solve equation
$x^{2} + 3x - 10 = 0$

Answer 1

${x}^{2} + 3 x - 10 = 0 \\ (x + 5)(x - 2) = 0 \\ x + 5 = 0 \: (or) \: \: x - 2 = 0 \\ \: x = - 5 \: \: \: \: (or) \: \: \: \: \: \: \: \: x = 2$
for better understanding in the first step please see factoring quadratic equation in khan academy

Answer 2

Hey there!!

We have:

... x²+3x-10=0

Now, let's split the middle term. We will have to split the middle term in a way that the terms we got have common in x³ and -10.

... x²+3x-10=0  

We will have to split 3x with the help of factor of -10.

... -10 = 5×(-2)

Hence, we can write the equation as:

... x² - 2x + 5x - 10 = 0

Taking common terms:

... x(x-2)-5(x-2)=0

... (x+5)(x-2)=0

Now, we have 2 equations

... x+5=0 and x-2=0

... x+5=0

... x=-5

... x-2=0

... x=2

Hence, the two answers of this equation are -5 and 2.

Hope my answer helps!