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Simplifying x2 + x + 2 = 5.75 Reorder the terms: 2 + x + x2 = 5.75 Solving 2 + x + x2 = 5.75 Solving for variable 'x'. Reorder the terms: 2 + -5.75 + x + x2 = 5.75 + -5.75 Combine like terms: 2 + -5.75 = -3.75 -3.75 + x + x2 = 5.75 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 -3.75 + x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + x + 3.75 + x2 = 0.00 + 3.75 Reorder the terms: -3.75 + 3.75 + x + x2 = 0.00 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x + x2 = 0.00 + 3.75 x + x2 = 0.00 + 3.75 Combine like terms: 0.00 + 3.75 = 3.75 x + x2 = 3.75 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 3.75 + 0.25 Reorder the terms: 0.25 + x + x2 = 3.75 + 0.25 Combine like terms: 3.75 + 0.25 = 4 0.25 + x + x2 = 4 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + 0.5) equal to 2 and -2.Subproblem 1
x + 0.5 = 2 Simplifying x + 0.5 = 2 Reorder the terms: 0.5 + x = 2 Solving 0.5 + x = 2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2 + -0.5 x = 2 + -0.5 Combine like terms: 2 + -0.5 = 1.5 x = 1.5 Simplifying x = 1.5Subproblem 2
x + 0.5 = -2 Simplifying x + 0.5 = -2 Reorder the terms: 0.5 + x = -2 Solving 0.5 + x = -2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2 + -0.5 x = -2 + -0.5 Combine like terms: -2 + -0.5 = -2.5 x = -2.5 Simplifying x = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5, -2.5}
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