First, let's simplify the expression:
2(x-6x)^2 + 120(x-3)^2 = 2(-5x)^2 + 120(x-3)^2= 2(25x^2) + 120(x^2 - 6x - 3x + 9)= 50x^2 + 120(x^2 - 9x + 9)
Now, distribute the 120:
50x^2 + 120x^2 - 1080x + 1080
Combine like terms:
170x^2 - 1080x + 1080 = 8
Subtract 8 from both sides:
170x^2 - 1080x + 1072 = 0
Now we have a quadratic equation:
We can simplify this equation further by dividing by 2:
85x^2 - 540x + 536 = 0
Now you can either use the quadratic formula, factoring, or another method to solve for x.
First, let's simplify the expression:
2(x-6x)^2 + 120(x-3)^2 = 2(-5x)^2 + 120(x-3)^2
= 2(25x^2) + 120(x^2 - 6x - 3x + 9)
= 50x^2 + 120(x^2 - 9x + 9)
Now, distribute the 120:
50x^2 + 120x^2 - 1080x + 1080
Combine like terms:
170x^2 - 1080x + 1080 = 8
Subtract 8 from both sides:
170x^2 - 1080x + 1072 = 0
Now we have a quadratic equation:
170x^2 - 1080x + 1072 = 0
We can simplify this equation further by dividing by 2:
85x^2 - 540x + 536 = 0
Now you can either use the quadratic formula, factoring, or another method to solve for x.