To find the values of x in the equation x² + 6x + 9 = 25, we first need to rearrange the equation. We can start by moving 25 to the left side of the equation:
x² + 6x + 9 – 25 = 0
This simplifies to:
x² + 6x – 16 = 0
Next, we can factor the quadratic equation. We need two numbers that multiply to -16 and add up to 6. The numbers that fit this requirement are 8 and -2. Therefore, we can rewrite the equation as:
(x + 8)(x – 2) = 0
Setting each factor equal to zero gives us the possible values for x:
x + 8 = 0
or
x – 2 = 0
From here, we solve each equation:
x + 8 = 0 → x = -8
x – 2 = 0 → x = 2
Therefore, the values of x in the equation x² + 6x + 9 = 25 are:
- x = -8
- x = 2