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Simplifying 0.5x2 + 2.75x = 1.5 Reorder the terms: 2.75x + 0.5x2 = 1.5 Solving 2.75x + 0.5x2 = 1.5 Solving for variable 'x'. Reorder the terms: -1.5 + 2.75x + 0.5x2 = 1.5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 -1.5 + 2.75x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -3 + 5.5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 5.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 5.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 5.5x + x2 = 0 + 3 5.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 5.5x + x2 = 3 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 3 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 3 + 7.5625 Combine like terms: 3 + 7.5625 = 10.5625 7.5625 + 5.5x + x2 = 10.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 10.5625 Calculate the square root of the right side: 3.25 Break this problem into two subproblems by setting (x + 2.75) equal to 3.25 and -3.25.Subproblem 1
x + 2.75 = 3.25 Simplifying x + 2.75 = 3.25 Reorder the terms: 2.75 + x = 3.25 Solving 2.75 + x = 3.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 3.25 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 3.25 + -2.75 x = 3.25 + -2.75 Combine like terms: 3.25 + -2.75 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + 2.75 = -3.25 Simplifying x + 2.75 = -3.25 Reorder the terms: 2.75 + x = -3.25 Solving 2.75 + x = -3.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -3.25 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -3.25 + -2.75 x = -3.25 + -2.75 Combine like terms: -3.25 + -2.75 = -6 x = -6 Simplifying x = -6Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, -6}
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