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Simplifying 0 = 19.4316x2 + -141.654x + 124.18 Reorder the terms: 0 = 124.18 + -141.654x + 19.4316x2 Solving 0 = 124.18 + -141.654x + 19.4316x2 Solving for variable 'x'. Combine like terms: 0 + -124.18 = -124.18 -124.18 + 141.654x + -19.4316x2 = 124.18 + -141.654x + 19.4316x2 + -124.18 + 141.654x + -19.4316x2 Reorder the terms: -124.18 + 141.654x + -19.4316x2 = 124.18 + -124.18 + -141.654x + 141.654x + 19.4316x2 + -19.4316x2 Combine like terms: 124.18 + -124.18 = 0.00 -124.18 + 141.654x + -19.4316x2 = 0.00 + -141.654x + 141.654x + 19.4316x2 + -19.4316x2 -124.18 + 141.654x + -19.4316x2 = -141.654x + 141.654x + 19.4316x2 + -19.4316x2 Combine like terms: -141.654x + 141.654x = 0.000 -124.18 + 141.654x + -19.4316x2 = 0.000 + 19.4316x2 + -19.4316x2 -124.18 + 141.654x + -19.4316x2 = 19.4316x2 + -19.4316x2 Combine like terms: 19.4316x2 + -19.4316x2 = 0.0000 -124.18 + 141.654x + -19.4316x2 = 0.0000 Begin completing the square. Divide all terms by -19.4316 the coefficient of the squared term: Divide each side by '-19.4316'. 6.390621462 + -7.289878342x + x2 = 0 Move the constant term to the right: Add '-6.390621462' to each side of the equation. 6.390621462 + -7.289878342x + -6.390621462 + x2 = 0 + -6.390621462 Reorder the terms: 6.390621462 + -6.390621462 + -7.289878342x + x2 = 0 + -6.390621462 Combine like terms: 6.390621462 + -6.390621462 = 0.000000000 0.000000000 + -7.289878342x + x2 = 0 + -6.390621462 -7.289878342x + x2 = 0 + -6.390621462 Combine like terms: 0 + -6.390621462 = -6.390621462 -7.289878342x + x2 = -6.390621462 The x term is -7.289878342x. Take half its coefficient (-3.644939171). Square it (13.28558156) and add it to both sides. Add '13.28558156' to each side of the equation. -7.289878342x + 13.28558156 + x2 = -6.390621462 + 13.28558156 Reorder the terms: 13.28558156 + -7.289878342x + x2 = -6.390621462 + 13.28558156 Combine like terms: -6.390621462 + 13.28558156 = 6.894960098 13.28558156 + -7.289878342x + x2 = 6.894960098 Factor a perfect square on the left side: (x + -3.644939171)(x + -3.644939171) = 6.894960098 Calculate the square root of the right side: 2.625825603 Break this problem into two subproblems by setting (x + -3.644939171) equal to 2.625825603 and -2.625825603.Subproblem 1
x + -3.644939171 = 2.625825603 Simplifying x + -3.644939171 = 2.625825603 Reorder the terms: -3.644939171 + x = 2.625825603 Solving -3.644939171 + x = 2.625825603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.644939171' to each side of the equation. -3.644939171 + 3.644939171 + x = 2.625825603 + 3.644939171 Combine like terms: -3.644939171 + 3.644939171 = 0.000000000 0.000000000 + x = 2.625825603 + 3.644939171 x = 2.625825603 + 3.644939171 Combine like terms: 2.625825603 + 3.644939171 = 6.270764774 x = 6.270764774 Simplifying x = 6.270764774Subproblem 2
x + -3.644939171 = -2.625825603 Simplifying x + -3.644939171 = -2.625825603 Reorder the terms: -3.644939171 + x = -2.625825603 Solving -3.644939171 + x = -2.625825603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.644939171' to each side of the equation. -3.644939171 + 3.644939171 + x = -2.625825603 + 3.644939171 Combine like terms: -3.644939171 + 3.644939171 = 0.000000000 0.000000000 + x = -2.625825603 + 3.644939171 x = -2.625825603 + 3.644939171 Combine like terms: -2.625825603 + 3.644939171 = 1.019113568 x = 1.019113568 Simplifying x = 1.019113568Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.270764774, 1.019113568}
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