Complete the square and write in graphing form.
2X^2=5x+12
To complete the square and write the equation in graphing form, follow these steps:
Step 1: Move the constant term to the right side of the equation:
2x^2 - 5x - 12 = 0
Step 2: Divide the entire equation by the coefficient of x^2 to make the leading coefficient 1:
x^2 - (5/2)x - 6 = 0
Step 3: Take half of the coefficient of x, square it, and add it to both sides of the equation:
x^2 - (5/2)x + (5/4)^2 = 6 + (5/4)^2
This is because (x - (5/4))^2 = x^2 - (5/2)x + (5/4)^2
Simplifying this gives:
x^2 - (5/2)x + 25/16 = 96/16 + 25/16
x^2 - (5/2)x + 25/16 = 121/16
Step 4: Factor the left side of the equation:
(x - 5/4)^2 = 121/16
Step 5: Take the square root of both sides of the equation:
x - 5/4 = ±√(121/16)
Step 6: Solve for x:
x - 5/4 = ±(11/4)
x = 5/4 ± 11/4
This gives two solutions:
x = (5 + 11)/4 = 16/4 = 4
x = (5 - 11)/4 = -6/4 = -3/2
So, the equation 2x^2 = 5x + 12, when completed and written in graphing form, becomes:
(x - 4)^2 = 121/16
Note: To write it in graphing form, you would usually move the constant term to the other side and write it in the standard form of a quadratic equation, but in this case, since we completed the square, the graphing form is already in the "vertex form" which is (x-h)^2 = k.