To solve the equation x² + 10x + 25 = 35, we first want to set it to 0. We do this by subtracting 35 from both sides:
x² + 10x + 25 – 35 = 0
This simplifies to:
x² + 10x – 10 = 0
Next, we can use the quadratic formula, which is x = (-b ± √(b² – 4ac)) / 2a, where a = 1, b = 10, and c = -10.
Calculating the discriminant (the part under the square root):
b² – 4ac = 10² – 4(1)(-10) = 100 + 40 = 140.
This gives us:
x = (-10 ± √140) / 2.
Now, we simplify √140. It can be simplified further since √140 = √(4 × 35) = 2√35.
So, the equation becomes:
x = (-10 ± 2√35) / 2.
Dividing everything by 2 gives us:
x = -5 ± √35.
Thus, the solutions for the equation x² + 10x + 25 = 35 are:
x = -5 + √35 and x = -5 – √35.