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Simplifying 121x + -5x2 = 102 + 29x Solving 121x + -5x2 = 102 + 29x Solving for variable 'x'. Reorder the terms: -102 + 121x + -29x + -5x2 = 102 + 29x + -102 + -29x Combine like terms: 121x + -29x = 92x -102 + 92x + -5x2 = 102 + 29x + -102 + -29x Reorder the terms: -102 + 92x + -5x2 = 102 + -102 + 29x + -29x Combine like terms: 102 + -102 = 0 -102 + 92x + -5x2 = 0 + 29x + -29x -102 + 92x + -5x2 = 29x + -29x Combine like terms: 29x + -29x = 0 -102 + 92x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 20.4 + -18.4x + x2 = 0 Move the constant term to the right: Add '-20.4' to each side of the equation. 20.4 + -18.4x + -20.4 + x2 = 0 + -20.4 Reorder the terms: 20.4 + -20.4 + -18.4x + x2 = 0 + -20.4 Combine like terms: 20.4 + -20.4 = 0.0 0.0 + -18.4x + x2 = 0 + -20.4 -18.4x + x2 = 0 + -20.4 Combine like terms: 0 + -20.4 = -20.4 -18.4x + x2 = -20.4 The x term is -18.4x. Take half its coefficient (-9.2). Square it (84.64) and add it to both sides. Add '84.64' to each side of the equation. -18.4x + 84.64 + x2 = -20.4 + 84.64 Reorder the terms: 84.64 + -18.4x + x2 = -20.4 + 84.64 Combine like terms: -20.4 + 84.64 = 64.24 84.64 + -18.4x + x2 = 64.24 Factor a perfect square on the left side: (x + -9.2)(x + -9.2) = 64.24 Calculate the square root of the right side: 8.014985964 Break this problem into two subproblems by setting (x + -9.2) equal to 8.014985964 and -8.014985964.Subproblem 1
x + -9.2 = 8.014985964 Simplifying x + -9.2 = 8.014985964 Reorder the terms: -9.2 + x = 8.014985964 Solving -9.2 + x = 8.014985964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.2' to each side of the equation. -9.2 + 9.2 + x = 8.014985964 + 9.2 Combine like terms: -9.2 + 9.2 = 0.0 0.0 + x = 8.014985964 + 9.2 x = 8.014985964 + 9.2 Combine like terms: 8.014985964 + 9.2 = 17.214985964 x = 17.214985964 Simplifying x = 17.214985964Subproblem 2
x + -9.2 = -8.014985964 Simplifying x + -9.2 = -8.014985964 Reorder the terms: -9.2 + x = -8.014985964 Solving -9.2 + x = -8.014985964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.2' to each side of the equation. -9.2 + 9.2 + x = -8.014985964 + 9.2 Combine like terms: -9.2 + 9.2 = 0.0 0.0 + x = -8.014985964 + 9.2 x = -8.014985964 + 9.2 Combine like terms: -8.014985964 + 9.2 = 1.185014036 x = 1.185014036 Simplifying x = 1.185014036Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.214985964, 1.185014036}
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