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Simplifying 1.01x2 + 0.25x + -1.5 = 0 Reorder the terms: -1.5 + 0.25x + 1.01x2 = 0 Solving -1.5 + 0.25x + 1.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.01 the coefficient of the squared term: Divide each side by '1.01'. -1.485148515 + 0.2475247525x + x2 = 0 Move the constant term to the right: Add '1.485148515' to each side of the equation. -1.485148515 + 0.2475247525x + 1.485148515 + x2 = 0 + 1.485148515 Reorder the terms: -1.485148515 + 1.485148515 + 0.2475247525x + x2 = 0 + 1.485148515 Combine like terms: -1.485148515 + 1.485148515 = 0.000000000 0.000000000 + 0.2475247525x + x2 = 0 + 1.485148515 0.2475247525x + x2 = 0 + 1.485148515 Combine like terms: 0 + 1.485148515 = 1.485148515 0.2475247525x + x2 = 1.485148515 The x term is 0.2475247525x. Take half its coefficient (0.1237623763). Square it (0.01531712579) and add it to both sides. Add '0.01531712579' to each side of the equation. 0.2475247525x + 0.01531712579 + x2 = 1.485148515 + 0.01531712579 Reorder the terms: 0.01531712579 + 0.2475247525x + x2 = 1.485148515 + 0.01531712579 Combine like terms: 1.485148515 + 0.01531712579 = 1.50046564079 0.01531712579 + 0.2475247525x + x2 = 1.50046564079 Factor a perfect square on the left side: (x + 0.1237623763)(x + 0.1237623763) = 1.50046564079 Calculate the square root of the right side: 1.224934954 Break this problem into two subproblems by setting (x + 0.1237623763) equal to 1.224934954 and -1.224934954.Subproblem 1
x + 0.1237623763 = 1.224934954 Simplifying x + 0.1237623763 = 1.224934954 Reorder the terms: 0.1237623763 + x = 1.224934954 Solving 0.1237623763 + x = 1.224934954 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1237623763' to each side of the equation. 0.1237623763 + -0.1237623763 + x = 1.224934954 + -0.1237623763 Combine like terms: 0.1237623763 + -0.1237623763 = 0.0000000000 0.0000000000 + x = 1.224934954 + -0.1237623763 x = 1.224934954 + -0.1237623763 Combine like terms: 1.224934954 + -0.1237623763 = 1.1011725777 x = 1.1011725777 Simplifying x = 1.1011725777Subproblem 2
x + 0.1237623763 = -1.224934954 Simplifying x + 0.1237623763 = -1.224934954 Reorder the terms: 0.1237623763 + x = -1.224934954 Solving 0.1237623763 + x = -1.224934954 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1237623763' to each side of the equation. 0.1237623763 + -0.1237623763 + x = -1.224934954 + -0.1237623763 Combine like terms: 0.1237623763 + -0.1237623763 = 0.0000000000 0.0000000000 + x = -1.224934954 + -0.1237623763 x = -1.224934954 + -0.1237623763 Combine like terms: -1.224934954 + -0.1237623763 = -1.3486973303 x = -1.3486973303 Simplifying x = -1.3486973303Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1011725777, -1.3486973303}
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