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Simplifying 40 = 0.01x2 + 0.344x + 28.74 Reorder the terms: 40 = 28.74 + 0.344x + 0.01x2 Solving 40 = 28.74 + 0.344x + 0.01x2 Solving for variable 'x'. Combine like terms: 40 + -28.74 = 11.26 11.26 + -0.344x + -0.01x2 = 28.74 + 0.344x + 0.01x2 + -28.74 + -0.344x + -0.01x2 Reorder the terms: 11.26 + -0.344x + -0.01x2 = 28.74 + -28.74 + 0.344x + -0.344x + 0.01x2 + -0.01x2 Combine like terms: 28.74 + -28.74 = 0.00 11.26 + -0.344x + -0.01x2 = 0.00 + 0.344x + -0.344x + 0.01x2 + -0.01x2 11.26 + -0.344x + -0.01x2 = 0.344x + -0.344x + 0.01x2 + -0.01x2 Combine like terms: 0.344x + -0.344x = 0.000 11.26 + -0.344x + -0.01x2 = 0.000 + 0.01x2 + -0.01x2 11.26 + -0.344x + -0.01x2 = 0.01x2 + -0.01x2 Combine like terms: 0.01x2 + -0.01x2 = 0.00 11.26 + -0.344x + -0.01x2 = 0.00 Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -1126 + 34.4x + x2 = 0 Move the constant term to the right: Add '1126' to each side of the equation. -1126 + 34.4x + 1126 + x2 = 0 + 1126 Reorder the terms: -1126 + 1126 + 34.4x + x2 = 0 + 1126 Combine like terms: -1126 + 1126 = 0 0 + 34.4x + x2 = 0 + 1126 34.4x + x2 = 0 + 1126 Combine like terms: 0 + 1126 = 1126 34.4x + x2 = 1126 The x term is 34.4x. Take half its coefficient (17.2). Square it (295.84) and add it to both sides. Add '295.84' to each side of the equation. 34.4x + 295.84 + x2 = 1126 + 295.84 Reorder the terms: 295.84 + 34.4x + x2 = 1126 + 295.84 Combine like terms: 1126 + 295.84 = 1421.84 295.84 + 34.4x + x2 = 1421.84 Factor a perfect square on the left side: (x + 17.2)(x + 17.2) = 1421.84 Calculate the square root of the right side: 37.707293724 Break this problem into two subproblems by setting (x + 17.2) equal to 37.707293724 and -37.707293724.Subproblem 1
x + 17.2 = 37.707293724 Simplifying x + 17.2 = 37.707293724 Reorder the terms: 17.2 + x = 37.707293724 Solving 17.2 + x = 37.707293724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.2' to each side of the equation. 17.2 + -17.2 + x = 37.707293724 + -17.2 Combine like terms: 17.2 + -17.2 = 0.0 0.0 + x = 37.707293724 + -17.2 x = 37.707293724 + -17.2 Combine like terms: 37.707293724 + -17.2 = 20.507293724 x = 20.507293724 Simplifying x = 20.507293724Subproblem 2
x + 17.2 = -37.707293724 Simplifying x + 17.2 = -37.707293724 Reorder the terms: 17.2 + x = -37.707293724 Solving 17.2 + x = -37.707293724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.2' to each side of the equation. 17.2 + -17.2 + x = -37.707293724 + -17.2 Combine like terms: 17.2 + -17.2 = 0.0 0.0 + x = -37.707293724 + -17.2 x = -37.707293724 + -17.2 Combine like terms: -37.707293724 + -17.2 = -54.907293724 x = -54.907293724 Simplifying x = -54.907293724Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.507293724, -54.907293724}
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