To use completing the square to determine the solutions to the equation 3x^2 - 24x + 40 = 28, we need to first rearrange the equation to isolate the x terms on one side:
3x^2 - 24x + 40 = 28
3x^2 - 24x + 12 = 0 [Subtract 28 from both sides]
Now, to complete the square, we want to rewrite this equation as a perfect square trinomial.
To do so, first divide the coefficient of x by 2 and square the result:
Coefficient of x = -24
(-24/2)^2 = (-12)^2 = 144
Now, add and subtract this number inside the parentheses:
3x^2 - 24x + 12
3(x^2 - 8x + 16) - 48 + 12 = 0
3(x - 4)^2 - 36 + 12 = 0
3(x - 4)^2 - 24 = 0
Now we can solve for x:
3(x - 4)^2 - 24 = 0
3(x - 4)^2 = 24
(x - 4)^2 = 8
x - 4 = ±√8
x = 4 ± √8
Therefore, the solutions to the equation 3x^2 - 24x + 40 = 28 are x = 4 + √8 and x = 4 - √8.
Use completing the square to determine which of the following gives the solutions to 3x2 − 24x + 40 = 28
1 answer