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Simplifying -1x2 + 443.432625675216x + -39.671192 = 0 Reorder the terms: -39.671192 + 443.432625675216x + -1x2 = 0 Solving -39.671192 + 443.432625675216x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 39.671192 + -443.4326257x + x2 = 0 Move the constant term to the right: Add '-39.671192' to each side of the equation. 39.671192 + -443.4326257x + -39.671192 + x2 = 0 + -39.671192 Reorder the terms: 39.671192 + -39.671192 + -443.4326257x + x2 = 0 + -39.671192 Combine like terms: 39.671192 + -39.671192 = 0.000000 0.000000 + -443.4326257x + x2 = 0 + -39.671192 -443.4326257x + x2 = 0 + -39.671192 Combine like terms: 0 + -39.671192 = -39.671192 -443.4326257x + x2 = -39.671192 The x term is -443.4326257x. Take half its coefficient (-221.7163129). Square it (49158.12341) and add it to both sides. Add '49158.12341' to each side of the equation. -443.4326257x + 49158.12341 + x2 = -39.671192 + 49158.12341 Reorder the terms: 49158.12341 + -443.4326257x + x2 = -39.671192 + 49158.12341 Combine like terms: -39.671192 + 49158.12341 = 49118.452218 49158.12341 + -443.4326257x + x2 = 49118.452218 Factor a perfect square on the left side: (x + -221.7163129)(x + -221.7163129) = 49118.452218 Calculate the square root of the right side: 221.626830998 Break this problem into two subproblems by setting (x + -221.7163129) equal to 221.626830998 and -221.626830998.Subproblem 1
x + -221.7163129 = 221.626830998 Simplifying x + -221.7163129 = 221.626830998 Reorder the terms: -221.7163129 + x = 221.626830998 Solving -221.7163129 + x = 221.626830998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '221.7163129' to each side of the equation. -221.7163129 + 221.7163129 + x = 221.626830998 + 221.7163129 Combine like terms: -221.7163129 + 221.7163129 = 0.0000000 0.0000000 + x = 221.626830998 + 221.7163129 x = 221.626830998 + 221.7163129 Combine like terms: 221.626830998 + 221.7163129 = 443.343143898 x = 443.343143898 Simplifying x = 443.343143898Subproblem 2
x + -221.7163129 = -221.626830998 Simplifying x + -221.7163129 = -221.626830998 Reorder the terms: -221.7163129 + x = -221.626830998 Solving -221.7163129 + x = -221.626830998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '221.7163129' to each side of the equation. -221.7163129 + 221.7163129 + x = -221.626830998 + 221.7163129 Combine like terms: -221.7163129 + 221.7163129 = 0.0000000 0.0000000 + x = -221.626830998 + 221.7163129 x = -221.626830998 + 221.7163129 Combine like terms: -221.626830998 + 221.7163129 = 0.089481902 x = 0.089481902 Simplifying x = 0.089481902Solution
The solution to the problem is based on the solutions from the subproblems. x = {443.343143898, 0.089481902}
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