I have to get this last problem done it's for my project here's the problem: solve by completing the square method
x 2- 12x =-11
X^2-12=-11
First add 11: x^2-12+11=0
Next: (x-11)(x-1)=0
Set each equal to 0: (x-11)=0 (x-1)=0
Get x alone by adding: x=11 x=1
Answer: (11,1)
Check work by plugging numbers into original equation.
x^2-12x=-11
x^2-12x=-11
(x-6)^2 -36=-11
(x-6)^2 = 36-11
(x-6)^2 =25
x-6 =+/-5
x = 6 +5 =11
x = 6 -5 =1
To solve the given equation using the completing the square method, you need to follow these steps:
1. Move the constant term (-11) to the right side of the equation:
x^2 - 12x = -11 + 0
This simplifies to: x^2 - 12x + 11 = 0
2. Take half of the coefficient of the x-term (-12) and square it. Add the result to both sides of the equation:
x^2 - 12x + (12/2)^2 = 11 + (12/2)^2
Simplifying further: x^2 - 12x + 36 = 11 + 36
This simplifies to: x^2 - 12x + 36 = 47
3. Factor the perfect square on the left side of the equation:
(x - 6)^2 = 47
4. Take the square root of both sides of the equation (be careful to consider both positive and negative square roots):
x - 6 = ± √47
5. Solve for x by isolating the variable:
x = 6 ± √47
So the solution to the equation x^2 - 12x = -11, using the completing the square method, is x = 6 ± √47.