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Simplifying 331x2 + x + -0.0250 = 0 Reorder the terms: -0.0250 + x + 331x2 = 0 Solving -0.0250 + x + 331x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 331 the coefficient of the squared term: Divide each side by '331'. -0.00007552870091 + 0.003021148036x + x2 = 0 Move the constant term to the right: Add '0.00007552870091' to each side of the equation. -0.00007552870091 + 0.003021148036x + 0.00007552870091 + x2 = 0 + 0.00007552870091 Reorder the terms: -0.00007552870091 + 0.00007552870091 + 0.003021148036x + x2 = 0 + 0.00007552870091 Combine like terms: -0.00007552870091 + 0.00007552870091 = 0.00000000000000 0.00000000000000 + 0.003021148036x + x2 = 0 + 0.00007552870091 0.003021148036x + x2 = 0 + 0.00007552870091 Combine like terms: 0 + 0.00007552870091 = 0.00007552870091 0.003021148036x + x2 = 0.00007552870091 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.003021148036x + 0.25 + x2 = 0.00007552870091 + 0.25 Reorder the terms: 0.25 + 0.003021148036x + x2 = 0.00007552870091 + 0.25 Combine like terms: 0.00007552870091 + 0.25 = 0.25007552870091 0.25 + 0.003021148036x + x2 = 0.25007552870091 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.25007552870091 Calculate the square root of the right side: 0.500075523 Break this problem into two subproblems by setting (x + 0.5) equal to 0.500075523 and -0.500075523.Subproblem 1
x + 0.5 = 0.500075523 Simplifying x + 0.5 = 0.500075523 Reorder the terms: 0.5 + x = 0.500075523 Solving 0.5 + x = 0.500075523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.500075523 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.500075523 + -0.5 x = 0.500075523 + -0.5 Combine like terms: 0.500075523 + -0.5 = 0.000075523 x = 0.000075523 Simplifying x = 0.000075523Subproblem 2
x + 0.5 = -0.500075523 Simplifying x + 0.5 = -0.500075523 Reorder the terms: 0.5 + x = -0.500075523 Solving 0.5 + x = -0.500075523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.500075523 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.500075523 + -0.5 x = -0.500075523 + -0.5 Combine like terms: -0.500075523 + -0.5 = -1.000075523 x = -1.000075523 Simplifying x = -1.000075523Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000075523, -1.000075523}
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