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Simplifying (9x2 + -5x + -37) + (2x2 + 9) = 0 Reorder the terms: (-37 + -5x + 9x2) + (2x2 + 9) = 0 Remove parenthesis around (-37 + -5x + 9x2) -37 + -5x + 9x2 + (2x2 + 9) = 0 Reorder the terms: -37 + -5x + 9x2 + (9 + 2x2) = 0 Remove parenthesis around (9 + 2x2) -37 + -5x + 9x2 + 9 + 2x2 = 0 Reorder the terms: -37 + 9 + -5x + 9x2 + 2x2 = 0 Combine like terms: -37 + 9 = -28 -28 + -5x + 9x2 + 2x2 = 0 Combine like terms: 9x2 + 2x2 = 11x2 -28 + -5x + 11x2 = 0 Solving -28 + -5x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -2.545454545 + -0.4545454545x + x2 = 0 Move the constant term to the right: Add '2.545454545' to each side of the equation. -2.545454545 + -0.4545454545x + 2.545454545 + x2 = 0 + 2.545454545 Reorder the terms: -2.545454545 + 2.545454545 + -0.4545454545x + x2 = 0 + 2.545454545 Combine like terms: -2.545454545 + 2.545454545 = 0.000000000 0.000000000 + -0.4545454545x + x2 = 0 + 2.545454545 -0.4545454545x + x2 = 0 + 2.545454545 Combine like terms: 0 + 2.545454545 = 2.545454545 -0.4545454545x + x2 = 2.545454545 The x term is -0.4545454545x. Take half its coefficient (-0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. -0.4545454545x + 0.05165289257 + x2 = 2.545454545 + 0.05165289257 Reorder the terms: 0.05165289257 + -0.4545454545x + x2 = 2.545454545 + 0.05165289257 Combine like terms: 2.545454545 + 0.05165289257 = 2.59710743757 0.05165289257 + -0.4545454545x + x2 = 2.59710743757 Factor a perfect square on the left side: (x + -0.2272727273)(x + -0.2272727273) = 2.59710743757 Calculate the square root of the right side: 1.611554355 Break this problem into two subproblems by setting (x + -0.2272727273) equal to 1.611554355 and -1.611554355.Subproblem 1
x + -0.2272727273 = 1.611554355 Simplifying x + -0.2272727273 = 1.611554355 Reorder the terms: -0.2272727273 + x = 1.611554355 Solving -0.2272727273 + x = 1.611554355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + x = 1.611554355 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + x = 1.611554355 + 0.2272727273 x = 1.611554355 + 0.2272727273 Combine like terms: 1.611554355 + 0.2272727273 = 1.8388270823 x = 1.8388270823 Simplifying x = 1.8388270823Subproblem 2
x + -0.2272727273 = -1.611554355 Simplifying x + -0.2272727273 = -1.611554355 Reorder the terms: -0.2272727273 + x = -1.611554355 Solving -0.2272727273 + x = -1.611554355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + x = -1.611554355 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + x = -1.611554355 + 0.2272727273 x = -1.611554355 + 0.2272727273 Combine like terms: -1.611554355 + 0.2272727273 = -1.3842816277 x = -1.3842816277 Simplifying x = -1.3842816277Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8388270823, -1.3842816277}
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