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Simplifying 9x2 + 42x + 37 = 0 Reorder the terms: 37 + 42x + 9x2 = 0 Solving 37 + 42x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 4.111111111 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '-4.111111111' to each side of the equation. 4.111111111 + 4.666666667x + -4.111111111 + x2 = 0 + -4.111111111 Reorder the terms: 4.111111111 + -4.111111111 + 4.666666667x + x2 = 0 + -4.111111111 Combine like terms: 4.111111111 + -4.111111111 = 0.000000000 0.000000000 + 4.666666667x + x2 = 0 + -4.111111111 4.666666667x + x2 = 0 + -4.111111111 Combine like terms: 0 + -4.111111111 = -4.111111111 4.666666667x + x2 = -4.111111111 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = -4.111111111 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = -4.111111111 + 5.444444448 Combine like terms: -4.111111111 + 5.444444448 = 1.333333337 5.444444448 + 4.666666667x + x2 = 1.333333337 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 1.333333337 Calculate the square root of the right side: 1.15470054 Break this problem into two subproblems by setting (x + 2.333333334) equal to 1.15470054 and -1.15470054.Subproblem 1
x + 2.333333334 = 1.15470054 Simplifying x + 2.333333334 = 1.15470054 Reorder the terms: 2.333333334 + x = 1.15470054 Solving 2.333333334 + x = 1.15470054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 1.15470054 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 1.15470054 + -2.333333334 x = 1.15470054 + -2.333333334 Combine like terms: 1.15470054 + -2.333333334 = -1.178632794 x = -1.178632794 Simplifying x = -1.178632794Subproblem 2
x + 2.333333334 = -1.15470054 Simplifying x + 2.333333334 = -1.15470054 Reorder the terms: 2.333333334 + x = -1.15470054 Solving 2.333333334 + x = -1.15470054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -1.15470054 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -1.15470054 + -2.333333334 x = -1.15470054 + -2.333333334 Combine like terms: -1.15470054 + -2.333333334 = -3.488033874 x = -3.488033874 Simplifying x = -3.488033874Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.178632794, -3.488033874}
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