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Simplifying 0.0001x2 + -0.05x + 1.6 = 0 Reorder the terms: 1.6 + -0.05x + 0.0001x2 = 0 Solving 1.6 + -0.05x + 0.0001x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0001 the coefficient of the squared term: Divide each side by '0.0001'. 16000 + -500x + x2 = 0 Move the constant term to the right: Add '-16000' to each side of the equation. 16000 + -500x + -16000 + x2 = 0 + -16000 Reorder the terms: 16000 + -16000 + -500x + x2 = 0 + -16000 Combine like terms: 16000 + -16000 = 0 0 + -500x + x2 = 0 + -16000 -500x + x2 = 0 + -16000 Combine like terms: 0 + -16000 = -16000 -500x + x2 = -16000 The x term is -500x. Take half its coefficient (-250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. -500x + 62500 + x2 = -16000 + 62500 Reorder the terms: 62500 + -500x + x2 = -16000 + 62500 Combine like terms: -16000 + 62500 = 46500 62500 + -500x + x2 = 46500 Factor a perfect square on the left side: (x + -250)(x + -250) = 46500 Calculate the square root of the right side: 215.638586528 Break this problem into two subproblems by setting (x + -250) equal to 215.638586528 and -215.638586528.Subproblem 1
x + -250 = 215.638586528 Simplifying x + -250 = 215.638586528 Reorder the terms: -250 + x = 215.638586528 Solving -250 + x = 215.638586528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = 215.638586528 + 250 Combine like terms: -250 + 250 = 0 0 + x = 215.638586528 + 250 x = 215.638586528 + 250 Combine like terms: 215.638586528 + 250 = 465.638586528 x = 465.638586528 Simplifying x = 465.638586528Subproblem 2
x + -250 = -215.638586528 Simplifying x + -250 = -215.638586528 Reorder the terms: -250 + x = -215.638586528 Solving -250 + x = -215.638586528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = -215.638586528 + 250 Combine like terms: -250 + 250 = 0 0 + x = -215.638586528 + 250 x = -215.638586528 + 250 Combine like terms: -215.638586528 + 250 = 34.361413472 x = 34.361413472 Simplifying x = 34.361413472Solution
The solution to the problem is based on the solutions from the subproblems. x = {465.638586528, 34.361413472}
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