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Simplifying 2x2 + 5x + -83 = 0 Reorder the terms: -83 + 5x + 2x2 = 0 Solving -83 + 5x + 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'. -41.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '41.5' to each side of the equation. -41.5 + 2.5x + 41.5 + x2 = 0 + 41.5 Reorder the terms: -41.5 + 41.5 + 2.5x + x2 = 0 + 41.5 Combine like terms: -41.5 + 41.5 = 0.0 0.0 + 2.5x + x2 = 0 + 41.5 2.5x + x2 = 0 + 41.5 Combine like terms: 0 + 41.5 = 41.5 2.5x + x2 = 41.5 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 = 41.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 41.5 + 1.5625 Combine like terms: 41.5 + 1.5625 = 43.0625 1.5625 + 2.5x + x2 = 43.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 43.0625 Calculate the square root of the right side: 6.562202374 Break this problem into two subproblems by setting (x + 1.25) equal to 6.562202374 and -6.562202374.Subproblem 1
x + 1.25 = 6.562202374 Simplifying x + 1.25 = 6.562202374 Reorder the terms: 1.25 + x = 6.562202374 Solving 1.25 + x = 6.562202374 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 = 6.562202374 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 6.562202374 + -1.25 x = 6.562202374 + -1.25 Combine like terms: 6.562202374 + -1.25 = 5.312202374 x = 5.312202374 Simplifying x = 5.312202374Subproblem 2
x + 1.25 = -6.562202374 Simplifying x + 1.25 = -6.562202374 Reorder the terms: 1.25 + x = -6.562202374 Solving 1.25 + x = -6.562202374 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 = -6.562202374 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -6.562202374 + -1.25 x = -6.562202374 + -1.25 Combine like terms: -6.562202374 + -1.25 = -7.812202374 x = -7.812202374 Simplifying x = -7.812202374Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.312202374, -7.812202374}
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