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Simplifying 9.35x2 + 1.97x + -7.42 = 0 Reorder the terms: -7.42 + 1.97x + 9.35x2 = 0 Solving -7.42 + 1.97x + 9.35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9.35 the coefficient of the squared term: Divide each side by '9.35'. -0.7935828877 + 0.2106951872x + x2 = 0 Move the constant term to the right: Add '0.7935828877' to each side of the equation. -0.7935828877 + 0.2106951872x + 0.7935828877 + x2 = 0 + 0.7935828877 Reorder the terms: -0.7935828877 + 0.7935828877 + 0.2106951872x + x2 = 0 + 0.7935828877 Combine like terms: -0.7935828877 + 0.7935828877 = 0.0000000000 0.0000000000 + 0.2106951872x + x2 = 0 + 0.7935828877 0.2106951872x + x2 = 0 + 0.7935828877 Combine like terms: 0 + 0.7935828877 = 0.7935828877 0.2106951872x + x2 = 0.7935828877 The x term is 0.2106951872x. Take half its coefficient (0.1053475936). Square it (0.01109811548) and add it to both sides. Add '0.01109811548' to each side of the equation. 0.2106951872x + 0.01109811548 + x2 = 0.7935828877 + 0.01109811548 Reorder the terms: 0.01109811548 + 0.2106951872x + x2 = 0.7935828877 + 0.01109811548 Combine like terms: 0.7935828877 + 0.01109811548 = 0.80468100318 0.01109811548 + 0.2106951872x + x2 = 0.80468100318 Factor a perfect square on the left side: (x + 0.1053475936)(x + 0.1053475936) = 0.80468100318 Calculate the square root of the right side: 0.897040135 Break this problem into two subproblems by setting (x + 0.1053475936) equal to 0.897040135 and -0.897040135.Subproblem 1
x + 0.1053475936 = 0.897040135 Simplifying x + 0.1053475936 = 0.897040135 Reorder the terms: 0.1053475936 + x = 0.897040135 Solving 0.1053475936 + x = 0.897040135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1053475936' to each side of the equation. 0.1053475936 + -0.1053475936 + x = 0.897040135 + -0.1053475936 Combine like terms: 0.1053475936 + -0.1053475936 = 0.0000000000 0.0000000000 + x = 0.897040135 + -0.1053475936 x = 0.897040135 + -0.1053475936 Combine like terms: 0.897040135 + -0.1053475936 = 0.7916925414 x = 0.7916925414 Simplifying x = 0.7916925414Subproblem 2
x + 0.1053475936 = -0.897040135 Simplifying x + 0.1053475936 = -0.897040135 Reorder the terms: 0.1053475936 + x = -0.897040135 Solving 0.1053475936 + x = -0.897040135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1053475936' to each side of the equation. 0.1053475936 + -0.1053475936 + x = -0.897040135 + -0.1053475936 Combine like terms: 0.1053475936 + -0.1053475936 = 0.0000000000 0.0000000000 + x = -0.897040135 + -0.1053475936 x = -0.897040135 + -0.1053475936 Combine like terms: -0.897040135 + -0.1053475936 = -1.0023877286 x = -1.0023877286 Simplifying x = -1.0023877286Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7916925414, -1.0023877286}
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