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Simplifying 0.276x2 + 0.05x + -0.014 = 0 Reorder the terms: -0.014 + 0.05x + 0.276x2 = 0 Solving -0.014 + 0.05x + 0.276x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.276 the coefficient of the squared term: Divide each side by '0.276'. -0.05072463768 + 0.1811594203x + x2 = 0 Move the constant term to the right: Add '0.05072463768' to each side of the equation. -0.05072463768 + 0.1811594203x + 0.05072463768 + x2 = 0 + 0.05072463768 Reorder the terms: -0.05072463768 + 0.05072463768 + 0.1811594203x + x2 = 0 + 0.05072463768 Combine like terms: -0.05072463768 + 0.05072463768 = 0.00000000000 0.00000000000 + 0.1811594203x + x2 = 0 + 0.05072463768 0.1811594203x + x2 = 0 + 0.05072463768 Combine like terms: 0 + 0.05072463768 = 0.05072463768 0.1811594203x + x2 = 0.05072463768 The x term is 0.1811594203x. Take half its coefficient (0.09057971015). Square it (0.008204683891) and add it to both sides. Add '0.008204683891' to each side of the equation. 0.1811594203x + 0.008204683891 + x2 = 0.05072463768 + 0.008204683891 Reorder the terms: 0.008204683891 + 0.1811594203x + x2 = 0.05072463768 + 0.008204683891 Combine like terms: 0.05072463768 + 0.008204683891 = 0.058929321571 0.008204683891 + 0.1811594203x + x2 = 0.058929321571 Factor a perfect square on the left side: (x + 0.09057971015)(x + 0.09057971015) = 0.058929321571 Calculate the square root of the right side: 0.242753623 Break this problem into two subproblems by setting (x + 0.09057971015) equal to 0.242753623 and -0.242753623.Subproblem 1
x + 0.09057971015 = 0.242753623 Simplifying x + 0.09057971015 = 0.242753623 Reorder the terms: 0.09057971015 + x = 0.242753623 Solving 0.09057971015 + x = 0.242753623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09057971015' to each side of the equation. 0.09057971015 + -0.09057971015 + x = 0.242753623 + -0.09057971015 Combine like terms: 0.09057971015 + -0.09057971015 = 0.00000000000 0.00000000000 + x = 0.242753623 + -0.09057971015 x = 0.242753623 + -0.09057971015 Combine like terms: 0.242753623 + -0.09057971015 = 0.15217391285 x = 0.15217391285 Simplifying x = 0.15217391285Subproblem 2
x + 0.09057971015 = -0.242753623 Simplifying x + 0.09057971015 = -0.242753623 Reorder the terms: 0.09057971015 + x = -0.242753623 Solving 0.09057971015 + x = -0.242753623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09057971015' to each side of the equation. 0.09057971015 + -0.09057971015 + x = -0.242753623 + -0.09057971015 Combine like terms: 0.09057971015 + -0.09057971015 = 0.00000000000 0.00000000000 + x = -0.242753623 + -0.09057971015 x = -0.242753623 + -0.09057971015 Combine like terms: -0.242753623 + -0.09057971015 = -0.33333333315 x = -0.33333333315 Simplifying x = -0.33333333315Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.15217391285, -0.33333333315}
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