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Simplifying 45x2 + -21x + -59 = 0 Reorder the terms: -59 + -21x + 45x2 = 0 Solving -59 + -21x + 45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -1.311111111 + -0.4666666667x + x2 = 0 Move the constant term to the right: Add '1.311111111' to each side of the equation. -1.311111111 + -0.4666666667x + 1.311111111 + x2 = 0 + 1.311111111 Reorder the terms: -1.311111111 + 1.311111111 + -0.4666666667x + x2 = 0 + 1.311111111 Combine like terms: -1.311111111 + 1.311111111 = 0.000000000 0.000000000 + -0.4666666667x + x2 = 0 + 1.311111111 -0.4666666667x + x2 = 0 + 1.311111111 Combine like terms: 0 + 1.311111111 = 1.311111111 -0.4666666667x + x2 = 1.311111111 The x term is -0.4666666667x. Take half its coefficient (-0.2333333334). Square it (0.05444444448) and add it to both sides. Add '0.05444444448' to each side of the equation. -0.4666666667x + 0.05444444448 + x2 = 1.311111111 + 0.05444444448 Reorder the terms: 0.05444444448 + -0.4666666667x + x2 = 1.311111111 + 0.05444444448 Combine like terms: 1.311111111 + 0.05444444448 = 1.36555555548 0.05444444448 + -0.4666666667x + x2 = 1.36555555548 Factor a perfect square on the left side: (x + -0.2333333334)(x + -0.2333333334) = 1.36555555548 Calculate the square root of the right side: 1.168569876 Break this problem into two subproblems by setting (x + -0.2333333334) equal to 1.168569876 and -1.168569876.Subproblem 1
x + -0.2333333334 = 1.168569876 Simplifying x + -0.2333333334 = 1.168569876 Reorder the terms: -0.2333333334 + x = 1.168569876 Solving -0.2333333334 + x = 1.168569876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2333333334' to each side of the equation. -0.2333333334 + 0.2333333334 + x = 1.168569876 + 0.2333333334 Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000 0.0000000000 + x = 1.168569876 + 0.2333333334 x = 1.168569876 + 0.2333333334 Combine like terms: 1.168569876 + 0.2333333334 = 1.4019032094 x = 1.4019032094 Simplifying x = 1.4019032094Subproblem 2
x + -0.2333333334 = -1.168569876 Simplifying x + -0.2333333334 = -1.168569876 Reorder the terms: -0.2333333334 + x = -1.168569876 Solving -0.2333333334 + x = -1.168569876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2333333334' to each side of the equation. -0.2333333334 + 0.2333333334 + x = -1.168569876 + 0.2333333334 Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000 0.0000000000 + x = -1.168569876 + 0.2333333334 x = -1.168569876 + 0.2333333334 Combine like terms: -1.168569876 + 0.2333333334 = -0.9352365426 x = -0.9352365426 Simplifying x = -0.9352365426Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4019032094, -0.9352365426}
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