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Simplifying 2x2 + 23x + 7 = 0 Reorder the terms: 7 + 23x + 2x2 = 0 Solving 7 + 23x + 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'. 3.5 + 11.5x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 11.5x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 11.5x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 11.5x + x2 = 0 + -3.5 11.5x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 11.5x + x2 = -3.5 The x term is 11.5x. Take half its coefficient (5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. 11.5x + 33.0625 + x2 = -3.5 + 33.0625 Reorder the terms: 33.0625 + 11.5x + x2 = -3.5 + 33.0625 Combine like terms: -3.5 + 33.0625 = 29.5625 33.0625 + 11.5x + x2 = 29.5625 Factor a perfect square on the left side: (x + 5.75)(x + 5.75) = 29.5625 Calculate the square root of the right side: 5.437140793 Break this problem into two subproblems by setting (x + 5.75) equal to 5.437140793 and -5.437140793.Subproblem 1
x + 5.75 = 5.437140793 Simplifying x + 5.75 = 5.437140793 Reorder the terms: 5.75 + x = 5.437140793 Solving 5.75 + x = 5.437140793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = 5.437140793 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = 5.437140793 + -5.75 x = 5.437140793 + -5.75 Combine like terms: 5.437140793 + -5.75 = -0.312859207 x = -0.312859207 Simplifying x = -0.312859207Subproblem 2
x + 5.75 = -5.437140793 Simplifying x + 5.75 = -5.437140793 Reorder the terms: 5.75 + x = -5.437140793 Solving 5.75 + x = -5.437140793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = -5.437140793 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = -5.437140793 + -5.75 x = -5.437140793 + -5.75 Combine like terms: -5.437140793 + -5.75 = -11.187140793 x = -11.187140793 Simplifying x = -11.187140793Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.312859207, -11.187140793}
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