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Simplifying (-2x2) + -5x + 5 = -50 Reorder the terms: 5 + -5x + (-2x2) = -50 Solving 5 + -5x + (-2x2) = -50 Solving for variable 'x'. Reorder the terms: 5 + 50 + -5x + (-2x2) = -50 + 50 Combine like terms: 5 + 50 = 55 55 + -5x + (-2x2) = -50 + 50 Combine like terms: -50 + 50 = 0 55 + -5x + (-2x2) = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -27.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + 2.5x + 27.5 + x2 = 0 + 27.5 Reorder the terms: -27.5 + 27.5 + 2.5x + x2 = 0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + 2.5x + x2 = 0 + 27.5 2.5x + x2 = 0 + 27.5 Combine like terms: 0 + 27.5 = 27.5 2.5x + x2 = 27.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 27.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 27.5 + 1.5625 Combine like terms: 27.5 + 1.5625 = 29.0625 1.5625 + 2.5x + x2 = 29.0625 Factor a perfect square on the left side: ((x) + 1.25)((x) + 1.25) = 29.0625 Calculate the square root of the right side: 5.390964663 Break this problem into two subproblems by setting ((x) + 1.25) equal to 5.390964663 and -5.390964663.Subproblem 1
(x) + 1.25 = 5.390964663 Simplifying (x) + 1.25 = 5.390964663 x + 1.25 = 5.390964663 Reorder the terms: 1.25 + x = 5.390964663 Solving 1.25 + x = 5.390964663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 5.390964663 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 5.390964663 + -1.25 x = 5.390964663 + -1.25 Combine like terms: 5.390964663 + -1.25 = 4.140964663 x = 4.140964663 Simplifying x = 4.140964663Subproblem 2
(x) + 1.25 = -5.390964663 Simplifying (x) + 1.25 = -5.390964663 x + 1.25 = -5.390964663 Reorder the terms: 1.25 + x = -5.390964663 Solving 1.25 + x = -5.390964663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -5.390964663 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -5.390964663 + -1.25 x = -5.390964663 + -1.25 Combine like terms: -5.390964663 + -1.25 = -6.640964663 x = -6.640964663 Simplifying x = -6.640964663Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.140964663, -6.640964663}
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