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Simplifying -38 = 3x(x + -6) + -5x Reorder the terms: -38 = 3x(-6 + x) + -5x -38 = (-6 * 3x + x * 3x) + -5x -38 = (-18x + 3x2) + -5x Reorder the terms: -38 = -18x + -5x + 3x2 Combine like terms: -18x + -5x = -23x -38 = -23x + 3x2 Solving -38 = -23x + 3x2 Solving for variable 'x'. Reorder the terms: -38 + 23x + -3x2 = -23x + 23x + 3x2 + -3x2 Combine like terms: -23x + 23x = 0 -38 + 23x + -3x2 = 0 + 3x2 + -3x2 -38 + 23x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -38 + 23x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 12.66666667 + -7.666666667x + x2 = 0 Move the constant term to the right: Add '-12.66666667' to each side of the equation. 12.66666667 + -7.666666667x + -12.66666667 + x2 = 0 + -12.66666667 Reorder the terms: 12.66666667 + -12.66666667 + -7.666666667x + x2 = 0 + -12.66666667 Combine like terms: 12.66666667 + -12.66666667 = 0.00000000 0.00000000 + -7.666666667x + x2 = 0 + -12.66666667 -7.666666667x + x2 = 0 + -12.66666667 Combine like terms: 0 + -12.66666667 = -12.66666667 -7.666666667x + x2 = -12.66666667 The x term is -7.666666667x. Take half its coefficient (-3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. -7.666666667x + 14.69444445 + x2 = -12.66666667 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667x + x2 = -12.66666667 + 14.69444445 Combine like terms: -12.66666667 + 14.69444445 = 2.02777778 14.69444445 + -7.666666667x + x2 = 2.02777778 Factor a perfect square on the left side: (x + -3.833333334)(x + -3.833333334) = 2.02777778 Calculate the square root of the right side: 1.424000625 Break this problem into two subproblems by setting (x + -3.833333334) equal to 1.424000625 and -1.424000625.Subproblem 1
x + -3.833333334 = 1.424000625 Simplifying x + -3.833333334 = 1.424000625 Reorder the terms: -3.833333334 + x = 1.424000625 Solving -3.833333334 + x = 1.424000625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = 1.424000625 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 1.424000625 + 3.833333334 x = 1.424000625 + 3.833333334 Combine like terms: 1.424000625 + 3.833333334 = 5.257333959 x = 5.257333959 Simplifying x = 5.257333959Subproblem 2
x + -3.833333334 = -1.424000625 Simplifying x + -3.833333334 = -1.424000625 Reorder the terms: -3.833333334 + x = -1.424000625 Solving -3.833333334 + x = -1.424000625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = -1.424000625 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -1.424000625 + 3.833333334 x = -1.424000625 + 3.833333334 Combine like terms: -1.424000625 + 3.833333334 = 2.409332709 x = 2.409332709 Simplifying x = 2.409332709Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.257333959, 2.409332709}
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