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Simplifying (x + -1.5)(x + -1.5) = 0 Reorder the terms: (-1.5 + x)(x + -1.5) = 0 Reorder the terms: (-1.5 + x)(-1.5 + x) = 0 Multiply (-1.5 + x) * (-1.5 + x) (-1.5(-1.5 + x) + x(-1.5 + x)) = 0 ((-1.5 * -1.5 + x * -1.5) + x(-1.5 + x)) = 0 ((2.25 + -1.5x) + x(-1.5 + x)) = 0 (2.25 + -1.5x + (-1.5 * x + x * x)) = 0 (2.25 + -1.5x + (-1.5x + x2)) = 0 Combine like terms: -1.5x + -1.5x = -3x (2.25 + -3x + x2) = 0 Solving 2.25 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -3x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -3x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -3x + x2 = 0 + -2.25 -3x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -3x + x2 = -2.25 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -2.25 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -2.25 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 2.25 + -3x + x2 = 0.00 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -1.5) equal to 0.00 and 0.00.Subproblem 1
x + -1.5 = 0.00 Simplifying x + -1.5 = 0.00 Reorder the terms: -1.5 + x = 0.00 Solving -1.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.00 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.00 + 1.5 x = 0.00 + 1.5 Combine like terms: 0.00 + 1.5 = 1.5 x = 1.5 Simplifying x = 1.5Subproblem 2
x + -1.5 = 0.00 Simplifying x + -1.5 = 0.00 Reorder the terms: -1.5 + x = 0.00 Solving -1.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.00 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.00 + 1.5 x = 0.00 + 1.5 Combine like terms: 0.00 + 1.5 = 1.5 x = 1.5 Simplifying x = 1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5, 1.5}
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