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Simplifying (5x2 + -5x + 18) + (9x2 + 7x + -71) = 0 Reorder the terms: (18 + -5x + 5x2) + (9x2 + 7x + -71) = 0 Remove parenthesis around (18 + -5x + 5x2) 18 + -5x + 5x2 + (9x2 + 7x + -71) = 0 Reorder the terms: 18 + -5x + 5x2 + (-71 + 7x + 9x2) = 0 Remove parenthesis around (-71 + 7x + 9x2) 18 + -5x + 5x2 + -71 + 7x + 9x2 = 0 Reorder the terms: 18 + -71 + -5x + 7x + 5x2 + 9x2 = 0 Combine like terms: 18 + -71 = -53 -53 + -5x + 7x + 5x2 + 9x2 = 0 Combine like terms: -5x + 7x = 2x -53 + 2x + 5x2 + 9x2 = 0 Combine like terms: 5x2 + 9x2 = 14x2 -53 + 2x + 14x2 = 0 Solving -53 + 2x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -3.785714286 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '3.785714286' to each side of the equation. -3.785714286 + 0.1428571429x + 3.785714286 + x2 = 0 + 3.785714286 Reorder the terms: -3.785714286 + 3.785714286 + 0.1428571429x + x2 = 0 + 3.785714286 Combine like terms: -3.785714286 + 3.785714286 = 0.000000000 0.000000000 + 0.1428571429x + x2 = 0 + 3.785714286 0.1428571429x + x2 = 0 + 3.785714286 Combine like terms: 0 + 3.785714286 = 3.785714286 0.1428571429x + x2 = 3.785714286 The x term is 0.1428571429x. Take half its coefficient (0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. 0.1428571429x + 0.005102040819 + x2 = 3.785714286 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429x + x2 = 3.785714286 + 0.005102040819 Combine like terms: 3.785714286 + 0.005102040819 = 3.790816326819 0.005102040819 + 0.1428571429x + x2 = 3.790816326819 Factor a perfect square on the left side: (x + 0.07142857145)(x + 0.07142857145) = 3.790816326819 Calculate the square root of the right side: 1.947001882 Break this problem into two subproblems by setting (x + 0.07142857145) equal to 1.947001882 and -1.947001882.Subproblem 1
x + 0.07142857145 = 1.947001882 Simplifying x + 0.07142857145 = 1.947001882 Reorder the terms: 0.07142857145 + x = 1.947001882 Solving 0.07142857145 + x = 1.947001882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = 1.947001882 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = 1.947001882 + -0.07142857145 x = 1.947001882 + -0.07142857145 Combine like terms: 1.947001882 + -0.07142857145 = 1.87557331055 x = 1.87557331055 Simplifying x = 1.87557331055Subproblem 2
x + 0.07142857145 = -1.947001882 Simplifying x + 0.07142857145 = -1.947001882 Reorder the terms: 0.07142857145 + x = -1.947001882 Solving 0.07142857145 + x = -1.947001882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = -1.947001882 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = -1.947001882 + -0.07142857145 x = -1.947001882 + -0.07142857145 Combine like terms: -1.947001882 + -0.07142857145 = -2.01843045345 x = -2.01843045345 Simplifying x = -2.01843045345Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.87557331055, -2.01843045345}
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