To solve the equation x² + 2x + 10 = 13, we start by rearranging it to set it to zero:
x² + 2x + 10 – 13 = 0
This simplifies to:
x² + 2x – 3 = 0
Now, we can factor this quadratic equation. We need two numbers that multiply to -3 and add to 2. Those numbers are 3 and -1. So we can express the equation as:
(x + 3)(x – 1) = 0
Setting each factor to zero gives us the possible solutions:
- x + 3 = 0 → x = -3
- x – 1 = 0 → x = 1
Thus, the solutions to the equation are x = -3 and x = 1. We can verify these by substituting back into the original equation:
For x = -3:
-3² + 2(-3) + 10 = 9 – 6 + 10 = 13
For x = 1:
1² + 2(1) + 10 = 1 + 2 + 10 = 13
Both solutions are valid, so the equation has two solutions: x = -3 and x = 1.