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Simplifying 0.01x2 + -6x + 5 = 0 Reorder the terms: 5 + -6x + 0.01x2 = 0 Solving 5 + -6x + 0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 500 + -600x + x2 = 0 Move the constant term to the right: Add '-500' to each side of the equation. 500 + -600x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + -600x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -600x + x2 = 0 + -500 -600x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 -600x + x2 = -500 The x term is -600x. Take half its coefficient (-300). Square it (90000) and add it to both sides. Add '90000' to each side of the equation. -600x + 90000 + x2 = -500 + 90000 Reorder the terms: 90000 + -600x + x2 = -500 + 90000 Combine like terms: -500 + 90000 = 89500 90000 + -600x + x2 = 89500 Factor a perfect square on the left side: (x + -300)(x + -300) = 89500 Calculate the square root of the right side: 299.165506033 Break this problem into two subproblems by setting (x + -300) equal to 299.165506033 and -299.165506033.Subproblem 1
x + -300 = 299.165506033 Simplifying x + -300 = 299.165506033 Reorder the terms: -300 + x = 299.165506033 Solving -300 + x = 299.165506033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = 299.165506033 + 300 Combine like terms: -300 + 300 = 0 0 + x = 299.165506033 + 300 x = 299.165506033 + 300 Combine like terms: 299.165506033 + 300 = 599.165506033 x = 599.165506033 Simplifying x = 599.165506033Subproblem 2
x + -300 = -299.165506033 Simplifying x + -300 = -299.165506033 Reorder the terms: -300 + x = -299.165506033 Solving -300 + x = -299.165506033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = -299.165506033 + 300 Combine like terms: -300 + 300 = 0 0 + x = -299.165506033 + 300 x = -299.165506033 + 300 Combine like terms: -299.165506033 + 300 = 0.834493967 x = 0.834493967 Simplifying x = 0.834493967Solution
The solution to the problem is based on the solutions from the subproblems. x = {599.165506033, 0.834493967}
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