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Simplifying 2x + 2x(22 + -3x) = 38 2x + (22 * 2x + -3x * 2x) = 38 2x + (44x + -6x2) = 38 Combine like terms: 2x + 44x = 46x 46x + -6x2 = 38 Solving 46x + -6x2 = 38 Solving for variable 'x'. Reorder the terms: -38 + 46x + -6x2 = 38 + -38 Combine like terms: 38 + -38 = 0 -38 + 46x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-19 + 23x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + 23x + -3x2)' equal to zero and attempt to solve: Simplifying -19 + 23x + -3x2 = 0 Solving -19 + 23x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 6.333333333 + -7.666666667x + x2 = 0 Move the constant term to the right: Add '-6.333333333' to each side of the equation. 6.333333333 + -7.666666667x + -6.333333333 + x2 = 0 + -6.333333333 Reorder the terms: 6.333333333 + -6.333333333 + -7.666666667x + x2 = 0 + -6.333333333 Combine like terms: 6.333333333 + -6.333333333 = 0.000000000 0.000000000 + -7.666666667x + x2 = 0 + -6.333333333 -7.666666667x + x2 = 0 + -6.333333333 Combine like terms: 0 + -6.333333333 = -6.333333333 -7.666666667x + x2 = -6.333333333 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 = -6.333333333 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667x + x2 = -6.333333333 + 14.69444445 Combine like terms: -6.333333333 + 14.69444445 = 8.361111117 14.69444445 + -7.666666667x + x2 = 8.361111117 Factor a perfect square on the left side: (x + -3.833333334)(x + -3.833333334) = 8.361111117 Calculate the square root of the right side: 2.891558597 Break this problem into two subproblems by setting (x + -3.833333334) equal to 2.891558597 and -2.891558597.Subproblem 1
x + -3.833333334 = 2.891558597 Simplifying x + -3.833333334 = 2.891558597 Reorder the terms: -3.833333334 + x = 2.891558597 Solving -3.833333334 + x = 2.891558597 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 = 2.891558597 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 2.891558597 + 3.833333334 x = 2.891558597 + 3.833333334 Combine like terms: 2.891558597 + 3.833333334 = 6.724891931 x = 6.724891931 Simplifying x = 6.724891931Subproblem 2
x + -3.833333334 = -2.891558597 Simplifying x + -3.833333334 = -2.891558597 Reorder the terms: -3.833333334 + x = -2.891558597 Solving -3.833333334 + x = -2.891558597 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 = -2.891558597 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -2.891558597 + 3.833333334 x = -2.891558597 + 3.833333334 Combine like terms: -2.891558597 + 3.833333334 = 0.941774737 x = 0.941774737 Simplifying x = 0.941774737Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.724891931, 0.941774737}Solution
x = {6.724891931, 0.941774737}
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