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Simplifying (9x2 + -5x + -42) + (4x2 + 7x) = 0 Reorder the terms: (-42 + -5x + 9x2) + (4x2 + 7x) = 0 Remove parenthesis around (-42 + -5x + 9x2) -42 + -5x + 9x2 + (4x2 + 7x) = 0 Reorder the terms: -42 + -5x + 9x2 + (7x + 4x2) = 0 Remove parenthesis around (7x + 4x2) -42 + -5x + 9x2 + 7x + 4x2 = 0 Reorder the terms: -42 + -5x + 7x + 9x2 + 4x2 = 0 Combine like terms: -5x + 7x = 2x -42 + 2x + 9x2 + 4x2 = 0 Combine like terms: 9x2 + 4x2 = 13x2 -42 + 2x + 13x2 = 0 Solving -42 + 2x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -3.230769231 + 0.1538461538x + x2 = 0 Move the constant term to the right: Add '3.230769231' to each side of the equation. -3.230769231 + 0.1538461538x + 3.230769231 + x2 = 0 + 3.230769231 Reorder the terms: -3.230769231 + 3.230769231 + 0.1538461538x + x2 = 0 + 3.230769231 Combine like terms: -3.230769231 + 3.230769231 = 0.000000000 0.000000000 + 0.1538461538x + x2 = 0 + 3.230769231 0.1538461538x + x2 = 0 + 3.230769231 Combine like terms: 0 + 3.230769231 = 3.230769231 0.1538461538x + x2 = 3.230769231 The x term is 0.1538461538x. Take half its coefficient (0.0769230769). Square it (0.005917159760) and add it to both sides. Add '0.005917159760' to each side of the equation. 0.1538461538x + 0.005917159760 + x2 = 3.230769231 + 0.005917159760 Reorder the terms: 0.005917159760 + 0.1538461538x + x2 = 3.230769231 + 0.005917159760 Combine like terms: 3.230769231 + 0.005917159760 = 3.23668639076 0.005917159760 + 0.1538461538x + x2 = 3.23668639076 Factor a perfect square on the left side: (x + 0.0769230769)(x + 0.0769230769) = 3.23668639076 Calculate the square root of the right side: 1.799079318 Break this problem into two subproblems by setting (x + 0.0769230769) equal to 1.799079318 and -1.799079318.Subproblem 1
x + 0.0769230769 = 1.799079318 Simplifying x + 0.0769230769 = 1.799079318 Reorder the terms: 0.0769230769 + x = 1.799079318 Solving 0.0769230769 + x = 1.799079318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + x = 1.799079318 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x = 1.799079318 + -0.0769230769 x = 1.799079318 + -0.0769230769 Combine like terms: 1.799079318 + -0.0769230769 = 1.7221562411 x = 1.7221562411 Simplifying x = 1.7221562411Subproblem 2
x + 0.0769230769 = -1.799079318 Simplifying x + 0.0769230769 = -1.799079318 Reorder the terms: 0.0769230769 + x = -1.799079318 Solving 0.0769230769 + x = -1.799079318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + x = -1.799079318 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x = -1.799079318 + -0.0769230769 x = -1.799079318 + -0.0769230769 Combine like terms: -1.799079318 + -0.0769230769 = -1.8760023949 x = -1.8760023949 Simplifying x = -1.8760023949Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7221562411, -1.8760023949}
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