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Simplifying x2 + 6 + -2x2 + 5x + -1 = 0 Reorder the terms: 6 + -1 + 5x + x2 + -2x2 = 0 Combine like terms: 6 + -1 = 5 5 + 5x + x2 + -2x2 = 0 Combine like terms: x2 + -2x2 = -1x2 5 + 5x + -1x2 = 0 Solving 5 + 5x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -5x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -5x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -5x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -5x + x2 = 0 + 5 -5x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -5x + x2 = 5 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 = 5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 5 + 6.25 Combine like terms: 5 + 6.25 = 11.25 6.25 + -5x + x2 = 11.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + -2.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x + -2.5 = 3.354101966 Simplifying x + -2.5 = 3.354101966 Reorder the terms: -2.5 + x = 3.354101966 Solving -2.5 + x = 3.354101966 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 = 3.354101966 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.354101966 + 2.5 x = 3.354101966 + 2.5 Combine like terms: 3.354101966 + 2.5 = 5.854101966 x = 5.854101966 Simplifying x = 5.854101966Subproblem 2
x + -2.5 = -3.354101966 Simplifying x + -2.5 = -3.354101966 Reorder the terms: -2.5 + x = -3.354101966 Solving -2.5 + x = -3.354101966 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 = -3.354101966 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.354101966 + 2.5 x = -3.354101966 + 2.5 Combine like terms: -3.354101966 + 2.5 = -0.854101966 x = -0.854101966 Simplifying x = -0.854101966Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.854101966, -0.854101966}
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