To solve the equation x² – 36 = 5x, we first rearrange the equation to set it to zero:
x² – 5x – 36 = 0
Now, we can apply the quadratic formula: x = (-b ± √(b² – 4ac)) / 2a, where a = 1, b = -5, and c = -36.
Calculating the discriminant (b² – 4ac):
b² = (-5)² = 25
4ac = 4 * 1 * -36 = -144
So, b² – 4ac = 25 + 144 = 169.
Now we can substitute back into the quadratic formula:
x = (5 ± √169) / 2
√169 = 13, so we have:
x = (5 + 13) / 2 or x = (5 – 13) / 2
This gives us two potential solutions:
x = 18 / 2 = 9 and x = -8 / 2 = -4.
Since we need the positive solution, the answer is:
x = 9