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Simplifying 12x2 + -44x + -7 = 0 Reorder the terms: -7 + -44x + 12x2 = 0 Solving -7 + -44x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.5833333333 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '0.5833333333' to each side of the equation. -0.5833333333 + -3.666666667x + 0.5833333333 + x2 = 0 + 0.5833333333 Reorder the terms: -0.5833333333 + 0.5833333333 + -3.666666667x + x2 = 0 + 0.5833333333 Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000 0.0000000000 + -3.666666667x + x2 = 0 + 0.5833333333 -3.666666667x + x2 = 0 + 0.5833333333 Combine like terms: 0 + 0.5833333333 = 0.5833333333 -3.666666667x + x2 = 0.5833333333 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = 0.5833333333 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 0.5833333333 + 3.361111114 Combine like terms: 0.5833333333 + 3.361111114 = 3.9444444473 3.361111114 + -3.666666667x + x2 = 3.9444444473 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 3.9444444473 Calculate the square root of the right side: 1.986062549 Break this problem into two subproblems by setting (x + -1.833333334) equal to 1.986062549 and -1.986062549.Subproblem 1
x + -1.833333334 = 1.986062549 Simplifying x + -1.833333334 = 1.986062549 Reorder the terms: -1.833333334 + x = 1.986062549 Solving -1.833333334 + x = 1.986062549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 1.986062549 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 1.986062549 + 1.833333334 x = 1.986062549 + 1.833333334 Combine like terms: 1.986062549 + 1.833333334 = 3.819395883 x = 3.819395883 Simplifying x = 3.819395883Subproblem 2
x + -1.833333334 = -1.986062549 Simplifying x + -1.833333334 = -1.986062549 Reorder the terms: -1.833333334 + x = -1.986062549 Solving -1.833333334 + x = -1.986062549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -1.986062549 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -1.986062549 + 1.833333334 x = -1.986062549 + 1.833333334 Combine like terms: -1.986062549 + 1.833333334 = -0.152729215 x = -0.152729215 Simplifying x = -0.152729215Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.819395883, -0.152729215}
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