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Simplifying 0.6x2 + -1.8x + 1.267 = 0 Reorder the terms: 1.267 + -1.8x + 0.6x2 = 0 Solving 1.267 + -1.8x + 0.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. 2.111666667 + -3x + x2 = 0 Move the constant term to the right: Add '-2.111666667' to each side of the equation. 2.111666667 + -3x + -2.111666667 + x2 = 0 + -2.111666667 Reorder the terms: 2.111666667 + -2.111666667 + -3x + x2 = 0 + -2.111666667 Combine like terms: 2.111666667 + -2.111666667 = 0.000000000 0.000000000 + -3x + x2 = 0 + -2.111666667 -3x + x2 = 0 + -2.111666667 Combine like terms: 0 + -2.111666667 = -2.111666667 -3x + x2 = -2.111666667 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -2.111666667 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -2.111666667 + 2.25 Combine like terms: -2.111666667 + 2.25 = 0.138333333 2.25 + -3x + x2 = 0.138333333 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.138333333 Calculate the square root of the right side: 0.371931893 Break this problem into two subproblems by setting (x + -1.5) equal to 0.371931893 and -0.371931893.Subproblem 1
x + -1.5 = 0.371931893 Simplifying x + -1.5 = 0.371931893 Reorder the terms: -1.5 + x = 0.371931893 Solving -1.5 + x = 0.371931893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.371931893 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.371931893 + 1.5 x = 0.371931893 + 1.5 Combine like terms: 0.371931893 + 1.5 = 1.871931893 x = 1.871931893 Simplifying x = 1.871931893Subproblem 2
x + -1.5 = -0.371931893 Simplifying x + -1.5 = -0.371931893 Reorder the terms: -1.5 + x = -0.371931893 Solving -1.5 + x = -0.371931893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.371931893 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.371931893 + 1.5 x = -0.371931893 + 1.5 Combine like terms: -0.371931893 + 1.5 = 1.128068107 x = 1.128068107 Simplifying x = 1.128068107Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.871931893, 1.128068107}
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