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Simplifying 2x2 + -11.5x = -7.5 Reorder the terms: -11.5x + 2x2 = -7.5 Solving -11.5x + 2x2 = -7.5 Solving for variable 'x'. Reorder the terms: 7.5 + -11.5x + 2x2 = -7.5 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 7.5 + -11.5x + 2x2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.75 + -5.75x + x2 = 0.0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -5.75x + -3.75 + x2 = 0.0 + -3.75 Reorder the terms: 3.75 + -3.75 + -5.75x + x2 = 0.0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -5.75x + x2 = 0.0 + -3.75 -5.75x + x2 = 0.0 + -3.75 Combine like terms: 0.0 + -3.75 = -3.75 -5.75x + x2 = -3.75 The x term is -5.75x. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75x + 8.265625 + x2 = -3.75 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = -3.75 + 8.265625 Combine like terms: -3.75 + 8.265625 = 4.515625 8.265625 + -5.75x + x2 = 4.515625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 4.515625 Calculate the square root of the right side: 2.125 Break this problem into two subproblems by setting (x + -2.875) equal to 2.125 and -2.125.Subproblem 1
x + -2.875 = 2.125 Simplifying x + -2.875 = 2.125 Reorder the terms: -2.875 + x = 2.125 Solving -2.875 + x = 2.125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = 2.125 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 2.125 + 2.875 x = 2.125 + 2.875 Combine like terms: 2.125 + 2.875 = 5 x = 5 Simplifying x = 5Subproblem 2
x + -2.875 = -2.125 Simplifying x + -2.875 = -2.125 Reorder the terms: -2.875 + x = -2.125 Solving -2.875 + x = -2.125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = -2.125 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -2.125 + 2.875 x = -2.125 + 2.875 Combine like terms: -2.125 + 2.875 = 0.75 x = 0.75 Simplifying x = 0.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, 0.75}
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