Answer:
- (x -6)² = 15
- x = 2.13 or 9.87
Step-by-step explanation:
It can help to understand what the square of a binomial looks like when you are asked to solve a quadratic by completing the square.
(x -a)² = x² -2ax +a²
In this form, the constant term a² is the square of half the x-coefficient. The x-coefficient and the constant in the binomial have the same sign.
Your quadratic is ...
x² -12x +21 = 0
It can be easier to complete the square if the given constant term is subtracted from both sides:
x² -12x = -21
Now, the square can be completed by adding the square of half the x-coefficient: (-12/2)² = (-6)² = 36.
x² -12x +36 = -21 +36
(x -6)² = 15 . . . . . . . . the form you want for your answer template
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Taking the square root gives ...
x -6 = ±√15
x = 6 ± √15 ≈ {2.13, 9.87} . . . . solutions to the equation
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Additional comment
The form we use for solving by completing the square is only one step away from "vertex form." That is, knowing the vertex of the function graph, we can write the vertex form equation, and find a solution immediately using the complete the square procedure.
vertex form equation: (x -6)² -15 = 0
form used for "complete the square" solution: (x -6)² = 15
