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Simplifying 100 = -0.4x2 + 57x + -13 Reorder the terms: 100 = -13 + 57x + -0.4x2 Solving 100 = -13 + 57x + -0.4x2 Solving for variable 'x'. Combine like terms: 100 + 13 = 113 113 + -57x + 0.4x2 = -13 + 57x + -0.4x2 + 13 + -57x + 0.4x2 Reorder the terms: 113 + -57x + 0.4x2 = -13 + 13 + 57x + -57x + -0.4x2 + 0.4x2 Combine like terms: -13 + 13 = 0 113 + -57x + 0.4x2 = 0 + 57x + -57x + -0.4x2 + 0.4x2 113 + -57x + 0.4x2 = 57x + -57x + -0.4x2 + 0.4x2 Combine like terms: 57x + -57x = 0 113 + -57x + 0.4x2 = 0 + -0.4x2 + 0.4x2 113 + -57x + 0.4x2 = -0.4x2 + 0.4x2 Combine like terms: -0.4x2 + 0.4x2 = 0.0 113 + -57x + 0.4x2 = 0.0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 282.5 + -142.5x + x2 = 0 Move the constant term to the right: Add '-282.5' to each side of the equation. 282.5 + -142.5x + -282.5 + x2 = 0 + -282.5 Reorder the terms: 282.5 + -282.5 + -142.5x + x2 = 0 + -282.5 Combine like terms: 282.5 + -282.5 = 0.0 0.0 + -142.5x + x2 = 0 + -282.5 -142.5x + x2 = 0 + -282.5 Combine like terms: 0 + -282.5 = -282.5 -142.5x + x2 = -282.5 The x term is -142.5x. Take half its coefficient (-71.25). Square it (5076.5625) and add it to both sides. Add '5076.5625' to each side of the equation. -142.5x + 5076.5625 + x2 = -282.5 + 5076.5625 Reorder the terms: 5076.5625 + -142.5x + x2 = -282.5 + 5076.5625 Combine like terms: -282.5 + 5076.5625 = 4794.0625 5076.5625 + -142.5x + x2 = 4794.0625 Factor a perfect square on the left side: (x + -71.25)(x + -71.25) = 4794.0625 Calculate the square root of the right side: 69.239168828 Break this problem into two subproblems by setting (x + -71.25) equal to 69.239168828 and -69.239168828.Subproblem 1
x + -71.25 = 69.239168828 Simplifying x + -71.25 = 69.239168828 Reorder the terms: -71.25 + x = 69.239168828 Solving -71.25 + x = 69.239168828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '71.25' to each side of the equation. -71.25 + 71.25 + x = 69.239168828 + 71.25 Combine like terms: -71.25 + 71.25 = 0.00 0.00 + x = 69.239168828 + 71.25 x = 69.239168828 + 71.25 Combine like terms: 69.239168828 + 71.25 = 140.489168828 x = 140.489168828 Simplifying x = 140.489168828Subproblem 2
x + -71.25 = -69.239168828 Simplifying x + -71.25 = -69.239168828 Reorder the terms: -71.25 + x = -69.239168828 Solving -71.25 + x = -69.239168828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '71.25' to each side of the equation. -71.25 + 71.25 + x = -69.239168828 + 71.25 Combine like terms: -71.25 + 71.25 = 0.00 0.00 + x = -69.239168828 + 71.25 x = -69.239168828 + 71.25 Combine like terms: -69.239168828 + 71.25 = 2.010831172 x = 2.010831172 Simplifying x = 2.010831172Solution
The solution to the problem is based on the solutions from the subproblems. x = {140.489168828, 2.010831172}
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