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Simplifying 4.9x2 + 6x + -650 = 0 Reorder the terms: -650 + 6x + 4.9x2 = 0 Solving -650 + 6x + 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'. -132.6530612 + 1.224489796x + x2 = 0 Move the constant term to the right: Add '132.6530612' to each side of the equation. -132.6530612 + 1.224489796x + 132.6530612 + x2 = 0 + 132.6530612 Reorder the terms: -132.6530612 + 132.6530612 + 1.224489796x + x2 = 0 + 132.6530612 Combine like terms: -132.6530612 + 132.6530612 = 0.0000000 0.0000000 + 1.224489796x + x2 = 0 + 132.6530612 1.224489796x + x2 = 0 + 132.6530612 Combine like terms: 0 + 132.6530612 = 132.6530612 1.224489796x + x2 = 132.6530612 The x term is 1.224489796x. Take half its coefficient (0.612244898). Square it (0.3748438151) and add it to both sides. Add '0.3748438151' to each side of the equation. 1.224489796x + 0.3748438151 + x2 = 132.6530612 + 0.3748438151 Reorder the terms: 0.3748438151 + 1.224489796x + x2 = 132.6530612 + 0.3748438151 Combine like terms: 132.6530612 + 0.3748438151 = 133.0279050151 0.3748438151 + 1.224489796x + x2 = 133.0279050151 Factor a perfect square on the left side: (x + 0.612244898)(x + 0.612244898) = 133.0279050151 Calculate the square root of the right side: 11.533772367 Break this problem into two subproblems by setting (x + 0.612244898) equal to 11.533772367 and -11.533772367.Subproblem 1
x + 0.612244898 = 11.533772367 Simplifying x + 0.612244898 = 11.533772367 Reorder the terms: 0.612244898 + x = 11.533772367 Solving 0.612244898 + x = 11.533772367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.612244898' to each side of the equation. 0.612244898 + -0.612244898 + x = 11.533772367 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + x = 11.533772367 + -0.612244898 x = 11.533772367 + -0.612244898 Combine like terms: 11.533772367 + -0.612244898 = 10.921527469 x = 10.921527469 Simplifying x = 10.921527469Subproblem 2
x + 0.612244898 = -11.533772367 Simplifying x + 0.612244898 = -11.533772367 Reorder the terms: 0.612244898 + x = -11.533772367 Solving 0.612244898 + x = -11.533772367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.612244898' to each side of the equation. 0.612244898 + -0.612244898 + x = -11.533772367 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + x = -11.533772367 + -0.612244898 x = -11.533772367 + -0.612244898 Combine like terms: -11.533772367 + -0.612244898 = -12.146017265 x = -12.146017265 Simplifying x = -12.146017265Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.921527469, -12.146017265}
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