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Simplifying (x + -0.25)(x + 6) = 0 Reorder the terms: (-0.25 + x)(x + 6) = 0 Reorder the terms: (-0.25 + x)(6 + x) = 0 Multiply (-0.25 + x) * (6 + x) (-0.25(6 + x) + x(6 + x)) = 0 ((6 * -0.25 + x * -0.25) + x(6 + x)) = 0 ((-1.5 + -0.25x) + x(6 + x)) = 0 (-1.5 + -0.25x + (6 * x + x * x)) = 0 (-1.5 + -0.25x + (6x + x2)) = 0 Combine like terms: -0.25x + 6x = 5.75x (-1.5 + 5.75x + x2) = 0 Solving -1.5 + 5.75x + 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 + 5.75x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 5.75x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 5.75x + x2 = 0 + 1.5 5.75x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 5.75x + x2 = 1.5 The x term is 5.75x. Take half its coefficient (2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. 5.75x + 8.265625 + x2 = 1.5 + 8.265625 Reorder the terms: 8.265625 + 5.75x + x2 = 1.5 + 8.265625 Combine like terms: 1.5 + 8.265625 = 9.765625 8.265625 + 5.75x + x2 = 9.765625 Factor a perfect square on the left side: (x + 2.875)(x + 2.875) = 9.765625 Calculate the square root of the right side: 3.125 Break this problem into two subproblems by setting (x + 2.875) equal to 3.125 and -3.125.Subproblem 1
x + 2.875 = 3.125 Simplifying x + 2.875 = 3.125 Reorder the terms: 2.875 + x = 3.125 Solving 2.875 + x = 3.125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = 3.125 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = 3.125 + -2.875 x = 3.125 + -2.875 Combine like terms: 3.125 + -2.875 = 0.25 x = 0.25 Simplifying x = 0.25Subproblem 2
x + 2.875 = -3.125 Simplifying x + 2.875 = -3.125 Reorder the terms: 2.875 + x = -3.125 Solving 2.875 + x = -3.125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = -3.125 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = -3.125 + -2.875 x = -3.125 + -2.875 Combine like terms: -3.125 + -2.875 = -6 x = -6 Simplifying x = -6Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.25, -6}
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