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Simplifying 950 + -4.9x2 + -2x = 0 Reorder the terms: 950 + -2x + -4.9x2 = 0 Solving 950 + -2x + -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 + 0.4081632653x + x2 = 0 Move the constant term to the right: Add '193.877551' to each side of the equation. -193.877551 + 0.4081632653x + 193.877551 + x2 = 0 + 193.877551 Reorder the terms: -193.877551 + 193.877551 + 0.4081632653x + x2 = 0 + 193.877551 Combine like terms: -193.877551 + 193.877551 = 0.000000 0.000000 + 0.4081632653x + x2 = 0 + 193.877551 0.4081632653x + x2 = 0 + 193.877551 Combine like terms: 0 + 193.877551 = 193.877551 0.4081632653x + x2 = 193.877551 The x term is 0.4081632653x. Take half its coefficient (0.2040816327). Square it (0.04164931281) and add it to both sides. Add '0.04164931281' to each side of the equation. 0.4081632653x + 0.04164931281 + x2 = 193.877551 + 0.04164931281 Reorder the terms: 0.04164931281 + 0.4081632653x + x2 = 193.877551 + 0.04164931281 Combine like terms: 193.877551 + 0.04164931281 = 193.91920031281 0.04164931281 + 0.4081632653x + x2 = 193.91920031281 Factor a perfect square on the left side: (x + 0.2040816327)(x + 0.2040816327) = 193.91920031281 Calculate the square root of the right side: 13.925487435 Break this problem into two subproblems by setting (x + 0.2040816327) equal to 13.925487435 and -13.925487435.Subproblem 1
x + 0.2040816327 = 13.925487435 Simplifying x + 0.2040816327 = 13.925487435 Reorder the terms: 0.2040816327 + x = 13.925487435 Solving 0.2040816327 + x = 13.925487435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2040816327' to each side of the equation. 0.2040816327 + -0.2040816327 + x = 13.925487435 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + x = 13.925487435 + -0.2040816327 x = 13.925487435 + -0.2040816327 Combine like terms: 13.925487435 + -0.2040816327 = 13.7214058023 x = 13.7214058023 Simplifying x = 13.7214058023Subproblem 2
x + 0.2040816327 = -13.925487435 Simplifying x + 0.2040816327 = -13.925487435 Reorder the terms: 0.2040816327 + x = -13.925487435 Solving 0.2040816327 + x = -13.925487435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2040816327' to each side of the equation. 0.2040816327 + -0.2040816327 + x = -13.925487435 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + x = -13.925487435 + -0.2040816327 x = -13.925487435 + -0.2040816327 Combine like terms: -13.925487435 + -0.2040816327 = -14.1295690677 x = -14.1295690677 Simplifying x = -14.1295690677Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.7214058023, -14.1295690677}
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