6×x2+7×x−3=0
how do i complete the squares in the quadratic formula? and how would i find the equation to graph
+23254 6x² +7x - 3 = 0
To complete the square:
Step 1) Move the constant term to the other side (add 3 to both sides):
6x² +7x = 3
Step 2) Divide all the terms by the coefficient of the squared term:
x² +(7/6)x = 1/2
Step 3) Divide the coefficient of the x-term by 2, square that number, and add that number to both sides:
7/6 ÷ 2 = 7/12 (7/12)² = 49/144
x² +(7/6)x + 49/144 = 1/2 + 49/144
x² +(7/6)x + 49/144 = 121/144
Step 4) Factor the left side:
(x + 7/12)² = 121/144
Step 5) Find the square root of both sides (don't forget the ± sign):
x + 7/12 = ± 11/12
Step 6) Finish:
x = -7/12 ± 11/12
x = 1/3, -3/2
+23254 6x² +7x - 3 = 0
To complete the square:
Step 1) Move the constant term to the other side (add 3 to both sides):
6x² +7x = 3
Step 2) Divide all the terms by the coefficient of the squared term:
x² +(7/6)x = 1/2
Step 3) Divide the coefficient of the x-term by 2, square that number, and add that number to both sides:
7/6 ÷ 2 = 7/12 (7/12)² = 49/144
x² +(7/6)x + 49/144 = 1/2 + 49/144
x² +(7/6)x + 49/144 = 121/144
Step 4) Factor the left side:
(x + 7/12)² = 121/144
Step 5) Find the square root of both sides (don't forget the ± sign):
x + 7/12 = ± 11/12
Step 6) Finish:
x = -7/12 ± 11/12
x = 1/3, -3/2
