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Simplifying -2x2 + 20x + -47 = 0 Reorder the terms: -47 + 20x + -2x2 = 0 Solving -47 + 20x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 23.5 + -10x + x2 = 0 Move the constant term to the right: Add '-23.5' to each side of the equation. 23.5 + -10x + -23.5 + x2 = 0 + -23.5 Reorder the terms: 23.5 + -23.5 + -10x + x2 = 0 + -23.5 Combine like terms: 23.5 + -23.5 = 0.0 0.0 + -10x + x2 = 0 + -23.5 -10x + x2 = 0 + -23.5 Combine like terms: 0 + -23.5 = -23.5 -10x + x2 = -23.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -23.5 + 25 Reorder the terms: 25 + -10x + x2 = -23.5 + 25 Combine like terms: -23.5 + 25 = 1.5 25 + -10x + x2 = 1.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + -5) equal to 1.224744871 and -1.224744871.Subproblem 1
x + -5 = 1.224744871 Simplifying x + -5 = 1.224744871 Reorder the terms: -5 + x = 1.224744871 Solving -5 + x = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 1.224744871 + 5 Combine like terms: -5 + 5 = 0 0 + x = 1.224744871 + 5 x = 1.224744871 + 5 Combine like terms: 1.224744871 + 5 = 6.224744871 x = 6.224744871 Simplifying x = 6.224744871Subproblem 2
x + -5 = -1.224744871 Simplifying x + -5 = -1.224744871 Reorder the terms: -5 + x = -1.224744871 Solving -5 + x = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -1.224744871 + 5 Combine like terms: -5 + 5 = 0 0 + x = -1.224744871 + 5 x = -1.224744871 + 5 Combine like terms: -1.224744871 + 5 = 3.775255129 x = 3.775255129 Simplifying x = 3.775255129Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.224744871, 3.775255129}
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