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Simplifying 12x2 + -44x = 50 Reorder the terms: -44x + 12x2 = 50 Solving -44x + 12x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + -44x + 12x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + -44x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + -22x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + -22x + 6x2)' equal to zero and attempt to solve: Simplifying -25 + -22x + 6x2 = 0 Solving -25 + -22x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -4.166666667 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '4.166666667' to each side of the equation. -4.166666667 + -3.666666667x + 4.166666667 + x2 = 0 + 4.166666667 Reorder the terms: -4.166666667 + 4.166666667 + -3.666666667x + x2 = 0 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + -3.666666667x + x2 = 0 + 4.166666667 -3.666666667x + x2 = 0 + 4.166666667 Combine like terms: 0 + 4.166666667 = 4.166666667 -3.666666667x + x2 = 4.166666667 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 = 4.166666667 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 4.166666667 + 3.361111114 Combine like terms: 4.166666667 + 3.361111114 = 7.527777781 3.361111114 + -3.666666667x + x2 = 7.527777781 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 7.527777781 Calculate the square root of the right side: 2.743679606 Break this problem into two subproblems by setting (x + -1.833333334) equal to 2.743679606 and -2.743679606.Subproblem 1
x + -1.833333334 = 2.743679606 Simplifying x + -1.833333334 = 2.743679606 Reorder the terms: -1.833333334 + x = 2.743679606 Solving -1.833333334 + x = 2.743679606 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 = 2.743679606 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 2.743679606 + 1.833333334 x = 2.743679606 + 1.833333334 Combine like terms: 2.743679606 + 1.833333334 = 4.57701294 x = 4.57701294 Simplifying x = 4.57701294Subproblem 2
x + -1.833333334 = -2.743679606 Simplifying x + -1.833333334 = -2.743679606 Reorder the terms: -1.833333334 + x = -2.743679606 Solving -1.833333334 + x = -2.743679606 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 = -2.743679606 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -2.743679606 + 1.833333334 x = -2.743679606 + 1.833333334 Combine like terms: -2.743679606 + 1.833333334 = -0.910346272 x = -0.910346272 Simplifying x = -0.910346272Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.57701294, -0.910346272}Solution
x = {4.57701294, -0.910346272}
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