Solve the quadratic equation by factoring:
x² + 10x + 13 = 4
Subtract 4 from both sides:
x² + 10x + 13 – 4 = 4 – 4
x² + 10x + 9 = 0
Now, look for two numbers so their sum is 10, and their product is 9. You can search within the set of the divisors of 9, for instance:
D(9) = {1, 3, 9}
Taking the numbers 1 and 9, you find that
• 1 + 9 = 10;
• 1 · 9 = 9.
So, in the equation, rewrite conveniently 10x as 9x + x, then it becomes
x² + 9x + x + 9 = 0
Factor the equation above by grouping. Take out the common factor x from the first two terms at the left-hand side:
x · (x + 9) + x + 9 = 0
x · (x + 9) + 1 · (x + 9) = 0
Now, take out the common factor (x + 9):
(x + 9) · (x + 1) = 0
If a product equals zero, the one of the factors must be zero:
x + 9 = 0 or x + 1 = 0
x = – 9 or x = – 1 <——— those are the solutions.
Solution set: S = {– 9, – 1}.
I hope this helps. =)