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Simplifying 20 = 20x + -4x2 + 1.5 Reorder the terms: 20 = 1.5 + 20x + -4x2 Solving 20 = 1.5 + 20x + -4x2 Solving for variable 'x'. Combine like terms: 20 + -1.5 = 18.5 18.5 + -20x + 4x2 = 1.5 + 20x + -4x2 + -1.5 + -20x + 4x2 Reorder the terms: 18.5 + -20x + 4x2 = 1.5 + -1.5 + 20x + -20x + -4x2 + 4x2 Combine like terms: 1.5 + -1.5 = 0.0 18.5 + -20x + 4x2 = 0.0 + 20x + -20x + -4x2 + 4x2 18.5 + -20x + 4x2 = 20x + -20x + -4x2 + 4x2 Combine like terms: 20x + -20x = 0 18.5 + -20x + 4x2 = 0 + -4x2 + 4x2 18.5 + -20x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 18.5 + -20x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.625 + -5x + x2 = 0 Move the constant term to the right: Add '-4.625' to each side of the equation. 4.625 + -5x + -4.625 + x2 = 0 + -4.625 Reorder the terms: 4.625 + -4.625 + -5x + x2 = 0 + -4.625 Combine like terms: 4.625 + -4.625 = 0.000 0.000 + -5x + x2 = 0 + -4.625 -5x + x2 = 0 + -4.625 Combine like terms: 0 + -4.625 = -4.625 -5x + x2 = -4.625 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -4.625 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -4.625 + 6.25 Combine like terms: -4.625 + 6.25 = 1.625 6.25 + -5x + x2 = 1.625 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 1.625 Calculate the square root of the right side: 1.274754878 Break this problem into two subproblems by setting (x + -2.5) equal to 1.274754878 and -1.274754878.Subproblem 1
x + -2.5 = 1.274754878 Simplifying x + -2.5 = 1.274754878 Reorder the terms: -2.5 + x = 1.274754878 Solving -2.5 + x = 1.274754878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.274754878 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.274754878 + 2.5 x = 1.274754878 + 2.5 Combine like terms: 1.274754878 + 2.5 = 3.774754878 x = 3.774754878 Simplifying x = 3.774754878Subproblem 2
x + -2.5 = -1.274754878 Simplifying x + -2.5 = -1.274754878 Reorder the terms: -2.5 + x = -1.274754878 Solving -2.5 + x = -1.274754878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.274754878 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.274754878 + 2.5 x = -1.274754878 + 2.5 Combine like terms: -1.274754878 + 2.5 = 1.225245122 x = 1.225245122 Simplifying x = 1.225245122Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.774754878, 1.225245122}
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