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Simplifying 14x + 5[6 + -1(2x + 3)] * 14x + 5[6 + -1(2x + 3)] = 0 Reorder the terms: 14x + 5[6 + -1(3 + 2x)] * 14x + 5[6 + -1(2x + 3)] = 0 14x + 5[6 + (3 * -1 + 2x * -1)] * 14x + 5[6 + -1(2x + 3)] = 0 14x + 5[6 + (-3 + -2x)] * 14x + 5[6 + -1(2x + 3)] = 0 Combine like terms: 6 + -3 = 3 14x + 5[3 + -2x] * 14x + 5[6 + -1(2x + 3)] = 0 Reorder the terms for easier multiplication: 14x + 5 * 14x[3 + -2x] + 5[6 + -1(2x + 3)] = 0 Multiply 5 * 14 14x + 70x[3 + -2x] + 5[6 + -1(2x + 3)] = 0 14x + [3 * 70x + -2x * 70x] + 5[6 + -1(2x + 3)] = 0 14x + [210x + -140x2] + 5[6 + -1(2x + 3)] = 0 Reorder the terms: 14x + 210x + -140x2 + 5[6 + -1(3 + 2x)] = 0 14x + 210x + -140x2 + 5[6 + (3 * -1 + 2x * -1)] = 0 14x + 210x + -140x2 + 5[6 + (-3 + -2x)] = 0 Combine like terms: 6 + -3 = 3 14x + 210x + -140x2 + 5[3 + -2x] = 0 14x + 210x + -140x2 + [3 * 5 + -2x * 5] = 0 14x + 210x + -140x2 + [15 + -10x] = 0 Reorder the terms: 15 + 14x + 210x + -10x + -140x2 = 0 Combine like terms: 14x + 210x = 224x 15 + 224x + -10x + -140x2 = 0 Combine like terms: 224x + -10x = 214x 15 + 214x + -140x2 = 0 Solving 15 + 214x + -140x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -140 the coefficient of the squared term: Divide each side by '-140'. -0.1071428571 + -1.528571429x + x2 = 0.0 Move the constant term to the right: Add '0.1071428571' to each side of the equation. -0.1071428571 + -1.528571429x + 0.1071428571 + x2 = 0.0 + 0.1071428571 Reorder the terms: -0.1071428571 + 0.1071428571 + -1.528571429x + x2 = 0.0 + 0.1071428571 Combine like terms: -0.1071428571 + 0.1071428571 = 0.0000000000 0.0000000000 + -1.528571429x + x2 = 0.0 + 0.1071428571 -1.528571429x + x2 = 0.0 + 0.1071428571 Combine like terms: 0.0 + 0.1071428571 = 0.1071428571 -1.528571429x + x2 = 0.1071428571 The x term is -1.528571429x. Take half its coefficient (-0.7642857145). Square it (0.5841326534) and add it to both sides. Add '0.5841326534' to each side of the equation. -1.528571429x + 0.5841326534 + x2 = 0.1071428571 + 0.5841326534 Reorder the terms: 0.5841326534 + -1.528571429x + x2 = 0.1071428571 + 0.5841326534 Combine like terms: 0.1071428571 + 0.5841326534 = 0.6912755105 0.5841326534 + -1.528571429x + x2 = 0.6912755105 Factor a perfect square on the left side: (x + -0.7642857145)(x + -0.7642857145) = 0.6912755105 Calculate the square root of the right side: 0.831429799 Break this problem into two subproblems by setting (x + -0.7642857145) equal to 0.831429799 and -0.831429799.Subproblem 1
x + -0.7642857145 = 0.831429799 Simplifying x + -0.7642857145 = 0.831429799 Reorder the terms: -0.7642857145 + x = 0.831429799 Solving -0.7642857145 + x = 0.831429799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7642857145' to each side of the equation. -0.7642857145 + 0.7642857145 + x = 0.831429799 + 0.7642857145 Combine like terms: -0.7642857145 + 0.7642857145 = 0.0000000000 0.0000000000 + x = 0.831429799 + 0.7642857145 x = 0.831429799 + 0.7642857145 Combine like terms: 0.831429799 + 0.7642857145 = 1.5957155135 x = 1.5957155135 Simplifying x = 1.5957155135Subproblem 2
x + -0.7642857145 = -0.831429799 Simplifying x + -0.7642857145 = -0.831429799 Reorder the terms: -0.7642857145 + x = -0.831429799 Solving -0.7642857145 + x = -0.831429799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7642857145' to each side of the equation. -0.7642857145 + 0.7642857145 + x = -0.831429799 + 0.7642857145 Combine like terms: -0.7642857145 + 0.7642857145 = 0.0000000000 0.0000000000 + x = -0.831429799 + 0.7642857145 x = -0.831429799 + 0.7642857145 Combine like terms: -0.831429799 + 0.7642857145 = -0.0671440845 x = -0.0671440845 Simplifying x = -0.0671440845Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5957155135, -0.0671440845}
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