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Simplifying (x + -0.57)(x + 0.5) = 0 Reorder the terms: (-0.57 + x)(x + 0.5) = 0 Reorder the terms: (-0.57 + x)(0.5 + x) = 0 Multiply (-0.57 + x) * (0.5 + x) (-0.57(0.5 + x) + x(0.5 + x)) = 0 ((0.5 * -0.57 + x * -0.57) + x(0.5 + x)) = 0 ((-0.285 + -0.57x) + x(0.5 + x)) = 0 (-0.285 + -0.57x + (0.5 * x + x * x)) = 0 (-0.285 + -0.57x + (0.5x + x2)) = 0 Combine like terms: -0.57x + 0.5x = -0.07x (-0.285 + -0.07x + x2) = 0 Solving -0.285 + -0.07x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.285' to each side of the equation. -0.285 + -0.07x + 0.285 + x2 = 0 + 0.285 Reorder the terms: -0.285 + 0.285 + -0.07x + x2 = 0 + 0.285 Combine like terms: -0.285 + 0.285 = 0.000 0.000 + -0.07x + x2 = 0 + 0.285 -0.07x + x2 = 0 + 0.285 Combine like terms: 0 + 0.285 = 0.285 -0.07x + x2 = 0.285 The x term is -0.07x. Take half its coefficient (-0.035). Square it (0.001225) and add it to both sides. Add '0.001225' to each side of the equation. -0.07x + 0.001225 + x2 = 0.285 + 0.001225 Reorder the terms: 0.001225 + -0.07x + x2 = 0.285 + 0.001225 Combine like terms: 0.285 + 0.001225 = 0.286225 0.001225 + -0.07x + x2 = 0.286225 Factor a perfect square on the left side: (x + -0.035)(x + -0.035) = 0.286225 Calculate the square root of the right side: 0.535 Break this problem into two subproblems by setting (x + -0.035) equal to 0.535 and -0.535.Subproblem 1
x + -0.035 = 0.535 Simplifying x + -0.035 = 0.535 Reorder the terms: -0.035 + x = 0.535 Solving -0.035 + x = 0.535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.035' to each side of the equation. -0.035 + 0.035 + x = 0.535 + 0.035 Combine like terms: -0.035 + 0.035 = 0.000 0.000 + x = 0.535 + 0.035 x = 0.535 + 0.035 Combine like terms: 0.535 + 0.035 = 0.57 x = 0.57 Simplifying x = 0.57Subproblem 2
x + -0.035 = -0.535 Simplifying x + -0.035 = -0.535 Reorder the terms: -0.035 + x = -0.535 Solving -0.035 + x = -0.535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.035' to each side of the equation. -0.035 + 0.035 + x = -0.535 + 0.035 Combine like terms: -0.035 + 0.035 = 0.000 0.000 + x = -0.535 + 0.035 x = -0.535 + 0.035 Combine like terms: -0.535 + 0.035 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.57, -0.5}
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