Solve x^2-6x+9
Using competing the square method
x^2-6x+9 is already a perfect square
... (x-3)^2
an equation is needed for a solution
This was answered for you on
February 26, 2018 at 11:26am
better go back and read it, rather than wasting time posting it -- incorrectly -- again!
To solve the equation x^2 - 6x + 9 using the completing the square method, follow these steps:
Step 1: Group the x^2 and x terms together:
x^2 - 6x + 9
Step 2: Take half of the coefficient of the x term (-6) and square it: (-6/2)^2 = 9
Step 3: Add and subtract the value obtained from step 2 inside the parentheses:
x^2 - 6x + 9 - 9
Step 4: Rearrange the expression to create a perfect square trinomial:
(x^2 - 6x + 9) - 9
Step 5: Simplify the expression inside the parentheses:
(x - 3)^2 - 9
Now we have transformed the equation into the form of a perfect square trinomial.
Step 6: Set the equation equal to zero:
(x - 3)^2 - 9 = 0
Step 7: Add 9 to both sides to eliminate the constant term on the left side:
(x - 3)^2 = 9
Step 8: Take the square root of both sides:
√((x - 3)^2) = ±√9
Step 9: Simplify the square root of 9:
(x - 3) = ±3
Step 10: Solve for x by isolating it:
x - 3 = 3 --> x = 3 + 3 --> x = 6
x - 3 = -3 --> x = -3 + 3 --> x = 0
Therefore, the solutions to the equation x^2 - 6x + 9 are x = 0 and x = 6.