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Simplifying 212x + -5000 + -1x2 = 0 Reorder the terms: -5000 + 212x + -1x2 = 0 Solving -5000 + 212x + -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'. 5000 + -212x + x2 = 0 Move the constant term to the right: Add '-5000' to each side of the equation. 5000 + -212x + -5000 + x2 = 0 + -5000 Reorder the terms: 5000 + -5000 + -212x + x2 = 0 + -5000 Combine like terms: 5000 + -5000 = 0 0 + -212x + x2 = 0 + -5000 -212x + x2 = 0 + -5000 Combine like terms: 0 + -5000 = -5000 -212x + x2 = -5000 The x term is -212x. Take half its coefficient (-106). Square it (11236) and add it to both sides. Add '11236' to each side of the equation. -212x + 11236 + x2 = -5000 + 11236 Reorder the terms: 11236 + -212x + x2 = -5000 + 11236 Combine like terms: -5000 + 11236 = 6236 11236 + -212x + x2 = 6236 Factor a perfect square on the left side: (x + -106)(x + -106) = 6236 Calculate the square root of the right side: 78.96834809 Break this problem into two subproblems by setting (x + -106) equal to 78.96834809 and -78.96834809.Subproblem 1
x + -106 = 78.96834809 Simplifying x + -106 = 78.96834809 Reorder the terms: -106 + x = 78.96834809 Solving -106 + x = 78.96834809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '106' to each side of the equation. -106 + 106 + x = 78.96834809 + 106 Combine like terms: -106 + 106 = 0 0 + x = 78.96834809 + 106 x = 78.96834809 + 106 Combine like terms: 78.96834809 + 106 = 184.96834809 x = 184.96834809 Simplifying x = 184.96834809Subproblem 2
x + -106 = -78.96834809 Simplifying x + -106 = -78.96834809 Reorder the terms: -106 + x = -78.96834809 Solving -106 + x = -78.96834809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '106' to each side of the equation. -106 + 106 + x = -78.96834809 + 106 Combine like terms: -106 + 106 = 0 0 + x = -78.96834809 + 106 x = -78.96834809 + 106 Combine like terms: -78.96834809 + 106 = 27.03165191 x = 27.03165191 Simplifying x = 27.03165191Solution
The solution to the problem is based on the solutions from the subproblems. x = {184.96834809, 27.03165191}
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