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Simplifying 0.0001185x2 + -0.01x + 0.0613 = 0 Reorder the terms: 0.0613 + -0.01x + 0.0001185x2 = 0 Solving 0.0613 + -0.01x + 0.0001185x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0001185 the coefficient of the squared term: Divide each side by '0.0001185'. 517.2995781 + -84.38818565x + x2 = 0 Move the constant term to the right: Add '-517.2995781' to each side of the equation. 517.2995781 + -84.38818565x + -517.2995781 + x2 = 0 + -517.2995781 Reorder the terms: 517.2995781 + -517.2995781 + -84.38818565x + x2 = 0 + -517.2995781 Combine like terms: 517.2995781 + -517.2995781 = 0.0000000 0.0000000 + -84.38818565x + x2 = 0 + -517.2995781 -84.38818565x + x2 = 0 + -517.2995781 Combine like terms: 0 + -517.2995781 = -517.2995781 -84.38818565x + x2 = -517.2995781 The x term is -84.38818565x. Take half its coefficient (-42.19409283). Square it (1780.341470) and add it to both sides. Add '1780.341470' to each side of the equation. -84.38818565x + 1780.341470 + x2 = -517.2995781 + 1780.341470 Reorder the terms: 1780.341470 + -84.38818565x + x2 = -517.2995781 + 1780.341470 Combine like terms: -517.2995781 + 1780.341470 = 1263.0418919 1780.341470 + -84.38818565x + x2 = 1263.0418919 Factor a perfect square on the left side: (x + -42.19409283)(x + -42.19409283) = 1263.0418919 Calculate the square root of the right side: 35.539300667 Break this problem into two subproblems by setting (x + -42.19409283) equal to 35.539300667 and -35.539300667.Subproblem 1
x + -42.19409283 = 35.539300667 Simplifying x + -42.19409283 = 35.539300667 Reorder the terms: -42.19409283 + x = 35.539300667 Solving -42.19409283 + x = 35.539300667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42.19409283' to each side of the equation. -42.19409283 + 42.19409283 + x = 35.539300667 + 42.19409283 Combine like terms: -42.19409283 + 42.19409283 = 0.00000000 0.00000000 + x = 35.539300667 + 42.19409283 x = 35.539300667 + 42.19409283 Combine like terms: 35.539300667 + 42.19409283 = 77.733393497 x = 77.733393497 Simplifying x = 77.733393497Subproblem 2
x + -42.19409283 = -35.539300667 Simplifying x + -42.19409283 = -35.539300667 Reorder the terms: -42.19409283 + x = -35.539300667 Solving -42.19409283 + x = -35.539300667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42.19409283' to each side of the equation. -42.19409283 + 42.19409283 + x = -35.539300667 + 42.19409283 Combine like terms: -42.19409283 + 42.19409283 = 0.00000000 0.00000000 + x = -35.539300667 + 42.19409283 x = -35.539300667 + 42.19409283 Combine like terms: -35.539300667 + 42.19409283 = 6.654792163 x = 6.654792163 Simplifying x = 6.654792163Solution
The solution to the problem is based on the solutions from the subproblems. x = {77.733393497, 6.654792163}
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