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Simplifying (x + -0.2)(x + 0.83) = 0 Reorder the terms: (-0.2 + x)(x + 0.83) = 0 Reorder the terms: (-0.2 + x)(0.83 + x) = 0 Multiply (-0.2 + x) * (0.83 + x) (-0.2(0.83 + x) + x(0.83 + x)) = 0 ((0.83 * -0.2 + x * -0.2) + x(0.83 + x)) = 0 ((-0.166 + -0.2x) + x(0.83 + x)) = 0 (-0.166 + -0.2x + (0.83 * x + x * x)) = 0 (-0.166 + -0.2x + (0.83x + x2)) = 0 Combine like terms: -0.2x + 0.83x = 0.63x (-0.166 + 0.63x + x2) = 0 Solving -0.166 + 0.63x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.166' to each side of the equation. -0.166 + 0.63x + 0.166 + x2 = 0 + 0.166 Reorder the terms: -0.166 + 0.166 + 0.63x + x2 = 0 + 0.166 Combine like terms: -0.166 + 0.166 = 0.000 0.000 + 0.63x + x2 = 0 + 0.166 0.63x + x2 = 0 + 0.166 Combine like terms: 0 + 0.166 = 0.166 0.63x + x2 = 0.166 The x term is 0.63x. Take half its coefficient (0.315). Square it (0.099225) and add it to both sides. Add '0.099225' to each side of the equation. 0.63x + 0.099225 + x2 = 0.166 + 0.099225 Reorder the terms: 0.099225 + 0.63x + x2 = 0.166 + 0.099225 Combine like terms: 0.166 + 0.099225 = 0.265225 0.099225 + 0.63x + x2 = 0.265225 Factor a perfect square on the left side: (x + 0.315)(x + 0.315) = 0.265225 Calculate the square root of the right side: 0.515 Break this problem into two subproblems by setting (x + 0.315) equal to 0.515 and -0.515.Subproblem 1
x + 0.315 = 0.515 Simplifying x + 0.315 = 0.515 Reorder the terms: 0.315 + x = 0.515 Solving 0.315 + x = 0.515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.315' to each side of the equation. 0.315 + -0.315 + x = 0.515 + -0.315 Combine like terms: 0.315 + -0.315 = 0.000 0.000 + x = 0.515 + -0.315 x = 0.515 + -0.315 Combine like terms: 0.515 + -0.315 = 0.2 x = 0.2 Simplifying x = 0.2Subproblem 2
x + 0.315 = -0.515 Simplifying x + 0.315 = -0.515 Reorder the terms: 0.315 + x = -0.515 Solving 0.315 + x = -0.515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.315' to each side of the equation. 0.315 + -0.315 + x = -0.515 + -0.315 Combine like terms: 0.315 + -0.315 = 0.000 0.000 + x = -0.515 + -0.315 x = -0.515 + -0.315 Combine like terms: -0.515 + -0.315 = -0.83 x = -0.83 Simplifying x = -0.83Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2, -0.83}
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