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Simplifying -4.9x2 + 7x + 950 = 0 Reorder the terms: 950 + 7x + -4.9x2 = 0 Solving 950 + 7x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -193.877551 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '193.877551' to each side of the equation. -193.877551 + -1.428571429x + 193.877551 + x2 = 0 + 193.877551 Reorder the terms: -193.877551 + 193.877551 + -1.428571429x + x2 = 0 + 193.877551 Combine like terms: -193.877551 + 193.877551 = 0.000000 0.000000 + -1.428571429x + x2 = 0 + 193.877551 -1.428571429x + x2 = 0 + 193.877551 Combine like terms: 0 + 193.877551 = 193.877551 -1.428571429x + x2 = 193.877551 The x term is -1.428571429x. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429x + 0.5102040819 + x2 = 193.877551 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 193.877551 + 0.5102040819 Combine like terms: 193.877551 + 0.5102040819 = 194.3877550819 0.5102040819 + -1.428571429x + x2 = 194.3877550819 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 194.3877550819 Calculate the square root of the right side: 13.942300925 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 13.942300925 and -13.942300925.Subproblem 1
x + -0.7142857145 = 13.942300925 Simplifying x + -0.7142857145 = 13.942300925 Reorder the terms: -0.7142857145 + x = 13.942300925 Solving -0.7142857145 + x = 13.942300925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = 13.942300925 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 13.942300925 + 0.7142857145 x = 13.942300925 + 0.7142857145 Combine like terms: 13.942300925 + 0.7142857145 = 14.6565866395 x = 14.6565866395 Simplifying x = 14.6565866395Subproblem 2
x + -0.7142857145 = -13.942300925 Simplifying x + -0.7142857145 = -13.942300925 Reorder the terms: -0.7142857145 + x = -13.942300925 Solving -0.7142857145 + x = -13.942300925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = -13.942300925 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -13.942300925 + 0.7142857145 x = -13.942300925 + 0.7142857145 Combine like terms: -13.942300925 + 0.7142857145 = -13.2280152105 x = -13.2280152105 Simplifying x = -13.2280152105Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.6565866395, -13.2280152105}
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