Solve the equation by completing the square.
x^2-12x+35=0
x^2-12x+35=0
x^2 - 12x = -35
x^2 - 12x + 36 = 36 - 35
(x - 6)^2 = 1
x - 6 = ± 1
x = 1+6 = 7
or
x = -1+6 = 5
adding 1 ... x^2 - 12 x + 36 = 1
taking √ ... x - 6 = ± 1
x = 7 , x = 5
Well, well, well, looks like we have a quadratic equation in the house! Let's solve x^2-12x+35=0 by completing the square and finding out what x is up to.
First things first, let's move that pesky constant term (35) to the other side to make our lives easier. We get:
x^2 - 12x = -35
Now, to complete the square, we want to take half of the coefficient of x (-12), square it, and add it to both sides of the equation. So, half of -12 is -6, and when we square it, we get 36. Adding 36 to both sides, we get:
x^2 - 12x + 36 = -35 + 36
(x - 6)^2 = 1
Now, take a look at that beautiful perfect square on the left-hand side! We can easily spot the square root of 1 is ±1. So, by taking the square root of both sides, we get:
x - 6 = ±1
Now, let's solve for x:
x = 6 ± 1
Drumroll, please! The solutions to x^2 - 12x + 35 = 0 are:
x = 7 or x = 5
I hope you enjoyed this little trip down quadratic lane!
To solve the given equation by completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation:
x^2 - 12x = -35
Step 2: Take half of the coefficient of x, square it, and add it to both sides of the equation:
x^2 - 12x + (-12/2)^2 = -35 + (-12/2)^2
x^2 - 12x + (6)^2 = -35 + (6)^2
x^2 - 12x + 36 = -35 + 36
Step 3: Simplify the equation:
x^2 - 12x + 36 = 1
Step 4: Rewrite the left side of the equation as a perfect square:
(x - 6)^2 = 1
Step 5: Take the square root of both sides of the equation:
√((x - 6)^2) = ±√1
x - 6 = ±1
Step 6: Solve for x:
x - 6 = 1 or x - 6 = -1
For x - 6 = 1:
x = 1 + 6
x = 7
For x - 6 = -1:
x = -1 + 6
x = 5
Therefore, the solutions to the equation x^2 - 12x + 35 = 0 are x = 7 and x = 5.