Solve by completing the square
12x^2+11x=5
divide by 12
x^2 + (11/12)x = 5/12
add the square of half the middle term coefficient
x^2 + 11x/12 + 121/576 = 5/12 + 121/576
(x + 11/24)^2 = 361/576
x+ 11/24 = ± √361/24
x = (-11 ± √361)/24
BTW, just noticed below that bobpursley did the same question for you yesterday
http://www.jiskha.com/display.cgi?id=1307404926
x^2+11/12x=5/12
x^2+2*(11/24)*x+(11/24)^2=5/12+(11/24)^2
(x+11/24)^2=(19/24)^2
x+11/24=19/24
or
x+11/24=-19/24
How silly of me not to notice that √361 = 19
Don't worry
sometimes it happens that 2*2=5
-6a-4=-7a+11=
To solve the equation 12x^2 + 11x = 5 by completing the square, follow these steps:
Step 1: Move the constant term to the right side of the equation:
12x^2 + 11x - 5 = 0
Step 2: Divide the entire equation by the coefficient of x^2 to make the coefficient 1:
x^2 + (11/12)x - 5/12 = 0
Step 3: Move the constant term to the right side of the equation, leaving a blank space:
x^2 + (11/12)x = 5/12
Step 4: Take half of the coefficient of x, square it, and add it to both sides of the equation. In this case, half of (11/12) is (11/24), and (11/24)^2 is (121/576):
x^2 + (11/12)x + (121/576) = 5/12 + (121/576)
Step 5: Simplify the right side of the equation:
x^2 + (11/12)x + (121/576) = 30/72 + 121/576
Step 6: Combine the fractions on the right side of the equation:
x^2 + (11/12)x + (121/576) = 605/720 + 121/576
Step 7: Find a common denominator and add the fractions:
x^2 + (11/12)x + (121/576) = 605/720 + 121/576
x^2 + (11/12)x + (121/576) = (605 + 121)/720
Step 8: Continue to simplify the right side of the equation:
x^2 + (11/12)x + (121/576) = 726/720
Step 9: Simplify the fraction on the right side of the equation:
x^2 + (11/12)x + (121/576) = 121/120
Step 10: Write the left side of the equation as a binomial squared by factoring:
(x + (11/24))^2 = 121/120
Step 11: Take the square root of both sides of the equation:
√[(x + (11/24))^2] = √(121/120)
Step 12: Solve for x by isolating it on one side of the equation:
x + (11/24) = ± √(121/120)
x = - (11/24) ± √(121/120)
Therefore, the solutions to the equation 12x^2 + 11x = 5 by completing the square are:
x = - (11/24) + √(121/120) and x = - (11/24) - √(121/120)