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Simplifying 18x2 + -48x + -50 = 0 Reorder the terms: -50 + -48x + 18x2 = 0 Solving -50 + -48x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + -24x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + -24x + 9x2)' equal to zero and attempt to solve: Simplifying -25 + -24x + 9x2 = 0 Solving -25 + -24x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.777777778 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '2.777777778' to each side of the equation. -2.777777778 + -2.666666667x + 2.777777778 + x2 = 0 + 2.777777778 Reorder the terms: -2.777777778 + 2.777777778 + -2.666666667x + x2 = 0 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + -2.666666667x + x2 = 0 + 2.777777778 -2.666666667x + x2 = 0 + 2.777777778 Combine like terms: 0 + 2.777777778 = 2.777777778 -2.666666667x + x2 = 2.777777778 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 2.777777778 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 2.777777778 + 1.777777780 Combine like terms: 2.777777778 + 1.777777780 = 4.555555558 1.777777780 + -2.666666667x + x2 = 4.555555558 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 4.555555558 Calculate the square root of the right side: 2.134374746 Break this problem into two subproblems by setting (x + -1.333333334) equal to 2.134374746 and -2.134374746.Subproblem 1
x + -1.333333334 = 2.134374746 Simplifying x + -1.333333334 = 2.134374746 Reorder the terms: -1.333333334 + x = 2.134374746 Solving -1.333333334 + x = 2.134374746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 2.134374746 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 2.134374746 + 1.333333334 x = 2.134374746 + 1.333333334 Combine like terms: 2.134374746 + 1.333333334 = 3.46770808 x = 3.46770808 Simplifying x = 3.46770808Subproblem 2
x + -1.333333334 = -2.134374746 Simplifying x + -1.333333334 = -2.134374746 Reorder the terms: -1.333333334 + x = -2.134374746 Solving -1.333333334 + x = -2.134374746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -2.134374746 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -2.134374746 + 1.333333334 x = -2.134374746 + 1.333333334 Combine like terms: -2.134374746 + 1.333333334 = -0.801041412 x = -0.801041412 Simplifying x = -0.801041412Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.46770808, -0.801041412}Solution
x = {3.46770808, -0.801041412}
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