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Simplifying (x + -0.5)(x + 4) = 0 Reorder the terms: (-0.5 + x)(x + 4) = 0 Reorder the terms: (-0.5 + x)(4 + x) = 0 Multiply (-0.5 + x) * (4 + x) (-0.5(4 + x) + x(4 + x)) = 0 ((4 * -0.5 + x * -0.5) + x(4 + x)) = 0 ((-2 + -0.5x) + x(4 + x)) = 0 (-2 + -0.5x + (4 * x + x * x)) = 0 (-2 + -0.5x + (4x + x2)) = 0 Combine like terms: -0.5x + 4x = 3.5x (-2 + 3.5x + x2) = 0 Solving -2 + 3.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 3.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 3.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3.5x + x2 = 0 + 2 3.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 3.5x + x2 = 2 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 = 2 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 2 + 3.0625 Combine like terms: 2 + 3.0625 = 5.0625 3.0625 + 3.5x + x2 = 5.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 5.0625 Calculate the square root of the right side: 2.25 Break this problem into two subproblems by setting (x + 1.75) equal to 2.25 and -2.25.Subproblem 1
x + 1.75 = 2.25 Simplifying x + 1.75 = 2.25 Reorder the terms: 1.75 + x = 2.25 Solving 1.75 + x = 2.25 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 = 2.25 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 2.25 + -1.75 x = 2.25 + -1.75 Combine like terms: 2.25 + -1.75 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + 1.75 = -2.25 Simplifying x + 1.75 = -2.25 Reorder the terms: 1.75 + x = -2.25 Solving 1.75 + x = -2.25 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 = -2.25 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -2.25 + -1.75 x = -2.25 + -1.75 Combine like terms: -2.25 + -1.75 = -4 x = -4 Simplifying x = -4Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, -4}
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