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Simplifying 2x2 + -5x + -124 = 0 Reorder the terms: -124 + -5x + 2x2 = 0 Solving -124 + -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'. -62 + -2.5x + x2 = 0 Move the constant term to the right: Add '62' to each side of the equation. -62 + -2.5x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + -2.5x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + -2.5x + x2 = 0 + 62 -2.5x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 -2.5x + x2 = 62 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 = 62 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 62 + 1.5625 Combine like terms: 62 + 1.5625 = 63.5625 1.5625 + -2.5x + x2 = 63.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 63.5625 Calculate the square root of the right side: 7.97260936 Break this problem into two subproblems by setting (x + -1.25) equal to 7.97260936 and -7.97260936.Subproblem 1
x + -1.25 = 7.97260936 Simplifying x + -1.25 = 7.97260936 Reorder the terms: -1.25 + x = 7.97260936 Solving -1.25 + x = 7.97260936 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 = 7.97260936 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 7.97260936 + 1.25 x = 7.97260936 + 1.25 Combine like terms: 7.97260936 + 1.25 = 9.22260936 x = 9.22260936 Simplifying x = 9.22260936Subproblem 2
x + -1.25 = -7.97260936 Simplifying x + -1.25 = -7.97260936 Reorder the terms: -1.25 + x = -7.97260936 Solving -1.25 + x = -7.97260936 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 = -7.97260936 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -7.97260936 + 1.25 x = -7.97260936 + 1.25 Combine like terms: -7.97260936 + 1.25 = -6.72260936 x = -6.72260936 Simplifying x = -6.72260936Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.22260936, -6.72260936}
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