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Simplifying -56x2 + 336x + -6 = 0 Reorder the terms: -6 + 336x + -56x2 = 0 Solving -6 + 336x + -56x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 168x + -28x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 168x + -28x2)' equal to zero and attempt to solve: Simplifying -3 + 168x + -28x2 = 0 Solving -3 + 168x + -28x2 = 0 Begin completing the square. Divide all terms by -28 the coefficient of the squared term: Divide each side by '-28'. 0.1071428571 + -6x + x2 = 0 Move the constant term to the right: Add '-0.1071428571' to each side of the equation. 0.1071428571 + -6x + -0.1071428571 + x2 = 0 + -0.1071428571 Reorder the terms: 0.1071428571 + -0.1071428571 + -6x + x2 = 0 + -0.1071428571 Combine like terms: 0.1071428571 + -0.1071428571 = 0.0000000000 0.0000000000 + -6x + x2 = 0 + -0.1071428571 -6x + x2 = 0 + -0.1071428571 Combine like terms: 0 + -0.1071428571 = -0.1071428571 -6x + x2 = -0.1071428571 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -0.1071428571 + 9 Reorder the terms: 9 + -6x + x2 = -0.1071428571 + 9 Combine like terms: -0.1071428571 + 9 = 8.8928571429 9 + -6x + x2 = 8.8928571429 Factor a perfect square on the left side: (x + -3)(x + -3) = 8.8928571429 Calculate the square root of the right side: 2.982089392 Break this problem into two subproblems by setting (x + -3) equal to 2.982089392 and -2.982089392.Subproblem 1
x + -3 = 2.982089392 Simplifying x + -3 = 2.982089392 Reorder the terms: -3 + x = 2.982089392 Solving -3 + x = 2.982089392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.982089392 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.982089392 + 3 x = 2.982089392 + 3 Combine like terms: 2.982089392 + 3 = 5.982089392 x = 5.982089392 Simplifying x = 5.982089392Subproblem 2
x + -3 = -2.982089392 Simplifying x + -3 = -2.982089392 Reorder the terms: -3 + x = -2.982089392 Solving -3 + x = -2.982089392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.982089392 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.982089392 + 3 x = -2.982089392 + 3 Combine like terms: -2.982089392 + 3 = 0.017910608 x = 0.017910608 Simplifying x = 0.017910608Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.982089392, 0.017910608}Solution
x = {5.982089392, 0.017910608}
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