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Simplifying 2x2 + 23x + -7.5 = 0 Reorder the terms: -7.5 + 23x + 2x2 = 0 Solving -7.5 + 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'. -3.75 + 11.5x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 11.5x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 11.5x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 11.5x + x2 = 0 + 3.75 11.5x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 11.5x + x2 = 3.75 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 = 3.75 + 33.0625 Reorder the terms: 33.0625 + 11.5x + x2 = 3.75 + 33.0625 Combine like terms: 3.75 + 33.0625 = 36.8125 33.0625 + 11.5x + x2 = 36.8125 Factor a perfect square on the left side: (x + 5.75)(x + 5.75) = 36.8125 Calculate the square root of the right side: 6.06733055 Break this problem into two subproblems by setting (x + 5.75) equal to 6.06733055 and -6.06733055.Subproblem 1
x + 5.75 = 6.06733055 Simplifying x + 5.75 = 6.06733055 Reorder the terms: 5.75 + x = 6.06733055 Solving 5.75 + x = 6.06733055 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 = 6.06733055 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = 6.06733055 + -5.75 x = 6.06733055 + -5.75 Combine like terms: 6.06733055 + -5.75 = 0.31733055 x = 0.31733055 Simplifying x = 0.31733055Subproblem 2
x + 5.75 = -6.06733055 Simplifying x + 5.75 = -6.06733055 Reorder the terms: 5.75 + x = -6.06733055 Solving 5.75 + x = -6.06733055 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 = -6.06733055 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = -6.06733055 + -5.75 x = -6.06733055 + -5.75 Combine like terms: -6.06733055 + -5.75 = -11.81733055 x = -11.81733055 Simplifying x = -11.81733055Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.31733055, -11.81733055}
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