To solve the equation x² – 20x + 100 = 36, we first rearrange it:
x² – 20x + 100 – 36 = 0
This simplifies to:
x² – 20x + 64 = 0
Next, we can apply the quadratic formula, which is:
x = (-b ± √(b² – 4ac)) / 2a
In our equation, the coefficients are:
- a = 1
- b = -20
- c = 64
Plugging these into the formula gives us:
x = (20 ± √((-20)² – 4 * 1 * 64)) / (2 * 1)
This simplifies down to:
x = (20 ± √(400 – 256)) / 2
Calculating inside the square root, we get:
x = (20 ± √144) / 2
Then we can find the square root of 144:
x = (20 ± 12) / 2
Now we can solve for the two possible values of x:
x₁ = (20 + 12) / 2 = 32 / 2 = 16
x₂ = (20 – 12) / 2 = 8 / 2 = 4
Thus, the solutions to the equation are:
- x = 16
- x = 4
These values satisfy the original equation. Therefore, the final answers for ‘x’ are 16 and 4.