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Simplifying 1.18 + 4.43x + -4.9x2 = 0 Solving 1.18 + 4.43x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.2408163265 + -0.9040816327x + x2 = 0 Move the constant term to the right: Add '0.2408163265' to each side of the equation. -0.2408163265 + -0.9040816327x + 0.2408163265 + x2 = 0 + 0.2408163265 Reorder the terms: -0.2408163265 + 0.2408163265 + -0.9040816327x + x2 = 0 + 0.2408163265 Combine like terms: -0.2408163265 + 0.2408163265 = 0.0000000000 0.0000000000 + -0.9040816327x + x2 = 0 + 0.2408163265 -0.9040816327x + x2 = 0 + 0.2408163265 Combine like terms: 0 + 0.2408163265 = 0.2408163265 -0.9040816327x + x2 = 0.2408163265 The x term is -0.9040816327x. Take half its coefficient (-0.4520408164). Square it (0.2043408997) and add it to both sides. Add '0.2043408997' to each side of the equation. -0.9040816327x + 0.2043408997 + x2 = 0.2408163265 + 0.2043408997 Reorder the terms: 0.2043408997 + -0.9040816327x + x2 = 0.2408163265 + 0.2043408997 Combine like terms: 0.2408163265 + 0.2043408997 = 0.4451572262 0.2043408997 + -0.9040816327x + x2 = 0.4451572262 Factor a perfect square on the left side: (x + -0.4520408164)(x + -0.4520408164) = 0.4451572262 Calculate the square root of the right side: 0.667201039 Break this problem into two subproblems by setting (x + -0.4520408164) equal to 0.667201039 and -0.667201039.Subproblem 1
x + -0.4520408164 = 0.667201039 Simplifying x + -0.4520408164 = 0.667201039 Reorder the terms: -0.4520408164 + x = 0.667201039 Solving -0.4520408164 + x = 0.667201039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4520408164' to each side of the equation. -0.4520408164 + 0.4520408164 + x = 0.667201039 + 0.4520408164 Combine like terms: -0.4520408164 + 0.4520408164 = 0.0000000000 0.0000000000 + x = 0.667201039 + 0.4520408164 x = 0.667201039 + 0.4520408164 Combine like terms: 0.667201039 + 0.4520408164 = 1.1192418554 x = 1.1192418554 Simplifying x = 1.1192418554Subproblem 2
x + -0.4520408164 = -0.667201039 Simplifying x + -0.4520408164 = -0.667201039 Reorder the terms: -0.4520408164 + x = -0.667201039 Solving -0.4520408164 + x = -0.667201039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4520408164' to each side of the equation. -0.4520408164 + 0.4520408164 + x = -0.667201039 + 0.4520408164 Combine like terms: -0.4520408164 + 0.4520408164 = 0.0000000000 0.0000000000 + x = -0.667201039 + 0.4520408164 x = -0.667201039 + 0.4520408164 Combine like terms: -0.667201039 + 0.4520408164 = -0.2151602226 x = -0.2151602226 Simplifying x = -0.2151602226Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1192418554, -0.2151602226}
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