Answers
y = 2
y = -5
Background
The general formula for a quadratic formula is the following:
ax² + bx + c = 0
The x values represent the variable (in the case of this question the variable would be "y" rather than x)
a, b, and c will change depending on the equation given
A factored equation will look as such:
(x + ___)(x + ___)
Step-by-Step
y² + 3y - 10 = 0
What are the a, b, and c in the given equation?
a = 1
b = 3
c = -10
In order to factor the equation you must find two numbers that BOTH add up to equal b AND multiply to equal c
What two numbers add to equal 3 AND multiply to equal -10?
-2 & 5
-2 + 5 = 3
-2 * 5 = -10
These numbers (- 2 and 5) will be the result of the factoring. Simply input the found answers into the factored format
(y + (-2))(y + 5)
(y - 2)(y + 5 )
To solve, you must set each individual factor equal to zero and solve for y:
Factor #1: (y - 2)
y - 2 = 0
y - 2 + 2 = 0 + 2
y = 2
Factor #2: (y +5)
y + 5 = 0
y + 5 - 5 = 0 - 5
y = -5
These are the answers or the zeros (where, if graphed, the equation will pass through these points on the x-axis)
y = 2
y = -5
Check
To make sure these answers are correct, substitute each y you solved into the y in the original equation. Solve using PEMDAS
2² + 3(2) - 10 = 0
4 + 6 - 10 = 0
10 - 10 = 0
0 = 0
(-5)² + 3(-5) - 10 = 0
25 + (-15) - 10 = 0
10 - 10 = 0
0 = 0
Both of the equations result in true values, thus the answers to this equation are:
y = -5
y = 2