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Simplifying x2 + 2x + 3 = 4.25 Reorder the terms: 3 + 2x + x2 = 4.25 Solving 3 + 2x + x2 = 4.25 Solving for variable 'x'. Reorder the terms: 3 + -4.25 + 2x + x2 = 4.25 + -4.25 Combine like terms: 3 + -4.25 = -1.25 -1.25 + 2x + x2 = 4.25 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 -1.25 + 2x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 2x + 1.25 + x2 = 0.00 + 1.25 Reorder the terms: -1.25 + 1.25 + 2x + x2 = 0.00 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 2x + x2 = 0.00 + 1.25 2x + x2 = 0.00 + 1.25 Combine like terms: 0.00 + 1.25 = 1.25 2x + x2 = 1.25 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 1.25 + 1 Reorder the terms: 1 + 2x + x2 = 1.25 + 1 Combine like terms: 1.25 + 1 = 2.25 1 + 2x + x2 = 2.25 Factor a perfect square on the left side: (x + 1)(x + 1) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (x + 1) equal to 1.5 and -1.5.Subproblem 1
x + 1 = 1.5 Simplifying x + 1 = 1.5 Reorder the terms: 1 + x = 1.5 Solving 1 + x = 1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.5 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.5 + -1 x = 1.5 + -1 Combine like terms: 1.5 + -1 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + 1 = -1.5 Simplifying x + 1 = -1.5 Reorder the terms: 1 + x = -1.5 Solving 1 + x = -1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.5 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.5 + -1 x = -1.5 + -1 Combine like terms: -1.5 + -1 = -2.5 x = -2.5 Simplifying x = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, -2.5}
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