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Simplifying 5.9X2 + -5.8X + 1.2 = 0 Reorder the terms: 1.2 + -5.8X + 5.9X2 = 0 Solving 1.2 + -5.8X + 5.9X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 5.9 the coefficient of the squared term: Divide each side by '5.9'. 0.2033898305 + -0.9830508475X + X2 = 0 Move the constant term to the right: Add '-0.2033898305' to each side of the equation. 0.2033898305 + -0.9830508475X + -0.2033898305 + X2 = 0 + -0.2033898305 Reorder the terms: 0.2033898305 + -0.2033898305 + -0.9830508475X + X2 = 0 + -0.2033898305 Combine like terms: 0.2033898305 + -0.2033898305 = 0.0000000000 0.0000000000 + -0.9830508475X + X2 = 0 + -0.2033898305 -0.9830508475X + X2 = 0 + -0.2033898305 Combine like terms: 0 + -0.2033898305 = -0.2033898305 -0.9830508475X + X2 = -0.2033898305 The X term is -0.9830508475X. Take half its coefficient (-0.4915254238). Square it (0.2415972422) and add it to both sides. Add '0.2415972422' to each side of the equation. -0.9830508475X + 0.2415972422 + X2 = -0.2033898305 + 0.2415972422 Reorder the terms: 0.2415972422 + -0.9830508475X + X2 = -0.2033898305 + 0.2415972422 Combine like terms: -0.2033898305 + 0.2415972422 = 0.0382074117 0.2415972422 + -0.9830508475X + X2 = 0.0382074117 Factor a perfect square on the left side: (X + -0.4915254238)(X + -0.4915254238) = 0.0382074117 Calculate the square root of the right side: 0.195467163 Break this problem into two subproblems by setting (X + -0.4915254238) equal to 0.195467163 and -0.195467163.Subproblem 1
X + -0.4915254238 = 0.195467163 Simplifying X + -0.4915254238 = 0.195467163 Reorder the terms: -0.4915254238 + X = 0.195467163 Solving -0.4915254238 + X = 0.195467163 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.4915254238' to each side of the equation. -0.4915254238 + 0.4915254238 + X = 0.195467163 + 0.4915254238 Combine like terms: -0.4915254238 + 0.4915254238 = 0.0000000000 0.0000000000 + X = 0.195467163 + 0.4915254238 X = 0.195467163 + 0.4915254238 Combine like terms: 0.195467163 + 0.4915254238 = 0.6869925868 X = 0.6869925868 Simplifying X = 0.6869925868Subproblem 2
X + -0.4915254238 = -0.195467163 Simplifying X + -0.4915254238 = -0.195467163 Reorder the terms: -0.4915254238 + X = -0.195467163 Solving -0.4915254238 + X = -0.195467163 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.4915254238' to each side of the equation. -0.4915254238 + 0.4915254238 + X = -0.195467163 + 0.4915254238 Combine like terms: -0.4915254238 + 0.4915254238 = 0.0000000000 0.0000000000 + X = -0.195467163 + 0.4915254238 X = -0.195467163 + 0.4915254238 Combine like terms: -0.195467163 + 0.4915254238 = 0.2960582608 X = 0.2960582608 Simplifying X = 0.2960582608Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.6869925868, 0.2960582608}
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