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Simplifying x2 + 3.5x + 1.5 = 0 Reorder the terms: 1.5 + 3.5x + x2 = 0 Solving 1.5 + 3.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 3.5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 3.5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 3.5x + x2 = 0 + -1.5 3.5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 3.5x + x2 = -1.5 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = -1.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -1.5 + 3.0625 Combine like terms: -1.5 + 3.0625 = 1.5625 3.0625 + 3.5x + x2 = 1.5625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 1.5625 Calculate the square root of the right side: 1.25 Break this problem into two subproblems by setting (x + 1.75) equal to 1.25 and -1.25.Subproblem 1
x + 1.75 = 1.25 Simplifying x + 1.75 = 1.25 Reorder the terms: 1.75 + x = 1.25 Solving 1.75 + x = 1.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 1.25 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 1.25 + -1.75 x = 1.25 + -1.75 Combine like terms: 1.25 + -1.75 = -0.5 x = -0.5 Simplifying x = -0.5Subproblem 2
x + 1.75 = -1.25 Simplifying x + 1.75 = -1.25 Reorder the terms: 1.75 + x = -1.25 Solving 1.75 + x = -1.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -1.25 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -1.25 + -1.75 x = -1.25 + -1.75 Combine like terms: -1.25 + -1.75 = -3 x = -3 Simplifying x = -3Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.5, -3}
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