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Simplifying x2 + 3.60x + 3.24 = 0 Reorder the terms: 3.24 + 3.60x + x2 = 0 Solving 3.24 + 3.60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3.24' to each side of the equation. 3.24 + 3.60x + -3.24 + x2 = 0 + -3.24 Reorder the terms: 3.24 + -3.24 + 3.60x + x2 = 0 + -3.24 Combine like terms: 3.24 + -3.24 = 0.00 0.00 + 3.60x + x2 = 0 + -3.24 3.60x + x2 = 0 + -3.24 Combine like terms: 0 + -3.24 = -3.24 3.60x + x2 = -3.24 The x term is 3.60x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.60x + 3.24 + x2 = -3.24 + 3.24 Reorder the terms: 3.24 + 3.60x + x2 = -3.24 + 3.24 Combine like terms: -3.24 + 3.24 = 0.00 3.24 + 3.60x + x2 = 0.00 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + 1.8) equal to 0.00 and 0.00.Subproblem 1
x + 1.8 = 0.00 Simplifying x + 1.8 = 0.00 Reorder the terms: 1.8 + x = 0.00 Solving 1.8 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 0.00 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 0.00 + -1.8 x = 0.00 + -1.8 Combine like terms: 0.00 + -1.8 = -1.8 x = -1.8 Simplifying x = -1.8Subproblem 2
x + 1.8 = 0.00 Simplifying x + 1.8 = 0.00 Reorder the terms: 1.8 + x = 0.00 Solving 1.8 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 0.00 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 0.00 + -1.8 x = 0.00 + -1.8 Combine like terms: 0.00 + -1.8 = -1.8 x = -1.8 Simplifying x = -1.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.8, -1.8}
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