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Simplifying 0.003x2 + -0.04x + 0.12 = 0 Reorder the terms: 0.12 + -0.04x + 0.003x2 = 0 Solving 0.12 + -0.04x + 0.003x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.003 the coefficient of the squared term: Divide each side by '0.003'. 40 + -13.33333333x + x2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -13.33333333x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -13.33333333x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -13.33333333x + x2 = 0 + -40 -13.33333333x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -13.33333333x + x2 = -40 The x term is -13.33333333x. Take half its coefficient (-6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. -13.33333333x + 44.44444442 + x2 = -40 + 44.44444442 Reorder the terms: 44.44444442 + -13.33333333x + x2 = -40 + 44.44444442 Combine like terms: -40 + 44.44444442 = 4.44444442 44.44444442 + -13.33333333x + x2 = 4.44444442 Factor a perfect square on the left side: (x + -6.666666665)(x + -6.666666665) = 4.44444442 Calculate the square root of the right side: 2.108185101 Break this problem into two subproblems by setting (x + -6.666666665) equal to 2.108185101 and -2.108185101.Subproblem 1
x + -6.666666665 = 2.108185101 Simplifying x + -6.666666665 = 2.108185101 Reorder the terms: -6.666666665 + x = 2.108185101 Solving -6.666666665 + x = 2.108185101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = 2.108185101 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = 2.108185101 + 6.666666665 x = 2.108185101 + 6.666666665 Combine like terms: 2.108185101 + 6.666666665 = 8.774851766 x = 8.774851766 Simplifying x = 8.774851766Subproblem 2
x + -6.666666665 = -2.108185101 Simplifying x + -6.666666665 = -2.108185101 Reorder the terms: -6.666666665 + x = -2.108185101 Solving -6.666666665 + x = -2.108185101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = -2.108185101 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = -2.108185101 + 6.666666665 x = -2.108185101 + 6.666666665 Combine like terms: -2.108185101 + 6.666666665 = 4.558481564 x = 4.558481564 Simplifying x = 4.558481564Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.774851766, 4.558481564}
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