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Simplifying 13x(x + -6) = 7(x + -2) Reorder the terms: 13x(-6 + x) = 7(x + -2) (-6 * 13x + x * 13x) = 7(x + -2) (-78x + 13x2) = 7(x + -2) Reorder the terms: -78x + 13x2 = 7(-2 + x) -78x + 13x2 = (-2 * 7 + x * 7) -78x + 13x2 = (-14 + 7x) Solving -78x + 13x2 = -14 + 7x Solving for variable 'x'. Reorder the terms: 14 + -78x + -7x + 13x2 = -14 + 7x + 14 + -7x Combine like terms: -78x + -7x = -85x 14 + -85x + 13x2 = -14 + 7x + 14 + -7x Reorder the terms: 14 + -85x + 13x2 = -14 + 14 + 7x + -7x Combine like terms: -14 + 14 = 0 14 + -85x + 13x2 = 0 + 7x + -7x 14 + -85x + 13x2 = 7x + -7x Combine like terms: 7x + -7x = 0 14 + -85x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 1.076923077 + -6.538461538x + x2 = 0 Move the constant term to the right: Add '-1.076923077' to each side of the equation. 1.076923077 + -6.538461538x + -1.076923077 + x2 = 0 + -1.076923077 Reorder the terms: 1.076923077 + -1.076923077 + -6.538461538x + x2 = 0 + -1.076923077 Combine like terms: 1.076923077 + -1.076923077 = 0.000000000 0.000000000 + -6.538461538x + x2 = 0 + -1.076923077 -6.538461538x + x2 = 0 + -1.076923077 Combine like terms: 0 + -1.076923077 = -1.076923077 -6.538461538x + x2 = -1.076923077 The x term is -6.538461538x. Take half its coefficient (-3.269230769). Square it (10.68786982) and add it to both sides. Add '10.68786982' to each side of the equation. -6.538461538x + 10.68786982 + x2 = -1.076923077 + 10.68786982 Reorder the terms: 10.68786982 + -6.538461538x + x2 = -1.076923077 + 10.68786982 Combine like terms: -1.076923077 + 10.68786982 = 9.610946743 10.68786982 + -6.538461538x + x2 = 9.610946743 Factor a perfect square on the left side: (x + -3.269230769)(x + -3.269230769) = 9.610946743 Calculate the square root of the right side: 3.100152697 Break this problem into two subproblems by setting (x + -3.269230769) equal to 3.100152697 and -3.100152697.Subproblem 1
x + -3.269230769 = 3.100152697 Simplifying x + -3.269230769 = 3.100152697 Reorder the terms: -3.269230769 + x = 3.100152697 Solving -3.269230769 + x = 3.100152697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.269230769' to each side of the equation. -3.269230769 + 3.269230769 + x = 3.100152697 + 3.269230769 Combine like terms: -3.269230769 + 3.269230769 = 0.000000000 0.000000000 + x = 3.100152697 + 3.269230769 x = 3.100152697 + 3.269230769 Combine like terms: 3.100152697 + 3.269230769 = 6.369383466 x = 6.369383466 Simplifying x = 6.369383466Subproblem 2
x + -3.269230769 = -3.100152697 Simplifying x + -3.269230769 = -3.100152697 Reorder the terms: -3.269230769 + x = -3.100152697 Solving -3.269230769 + x = -3.100152697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.269230769' to each side of the equation. -3.269230769 + 3.269230769 + x = -3.100152697 + 3.269230769 Combine like terms: -3.269230769 + 3.269230769 = 0.000000000 0.000000000 + x = -3.100152697 + 3.269230769 x = -3.100152697 + 3.269230769 Combine like terms: -3.100152697 + 3.269230769 = 0.169078072 x = 0.169078072 Simplifying x = 0.169078072Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.369383466, 0.169078072}
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