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Simplifying 56x2 + -2x + -6 = 0 Reorder the terms: -6 + -2x + 56x2 = 0 Solving -6 + -2x + 56x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -1x + 28x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -1x + 28x2)' equal to zero and attempt to solve: Simplifying -3 + -1x + 28x2 = 0 Solving -3 + -1x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.1071428571 + -0.03571428571x + x2 = 0 Move the constant term to the right: Add '0.1071428571' to each side of the equation. -0.1071428571 + -0.03571428571x + 0.1071428571 + x2 = 0 + 0.1071428571 Reorder the terms: -0.1071428571 + 0.1071428571 + -0.03571428571x + x2 = 0 + 0.1071428571 Combine like terms: -0.1071428571 + 0.1071428571 = 0.0000000000 0.0000000000 + -0.03571428571x + x2 = 0 + 0.1071428571 -0.03571428571x + x2 = 0 + 0.1071428571 Combine like terms: 0 + 0.1071428571 = 0.1071428571 -0.03571428571x + x2 = 0.1071428571 The x term is -0.03571428571x. Take half its coefficient (-0.01785714286). Square it (0.0003188775511) and add it to both sides. Add '0.0003188775511' to each side of the equation. -0.03571428571x + 0.0003188775511 + x2 = 0.1071428571 + 0.0003188775511 Reorder the terms: 0.0003188775511 + -0.03571428571x + x2 = 0.1071428571 + 0.0003188775511 Combine like terms: 0.1071428571 + 0.0003188775511 = 0.1074617346511 0.0003188775511 + -0.03571428571x + x2 = 0.1074617346511 Factor a perfect square on the left side: (x + -0.01785714286)(x + -0.01785714286) = 0.1074617346511 Calculate the square root of the right side: 0.327813567 Break this problem into two subproblems by setting (x + -0.01785714286) equal to 0.327813567 and -0.327813567.Subproblem 1
x + -0.01785714286 = 0.327813567 Simplifying x + -0.01785714286 = 0.327813567 Reorder the terms: -0.01785714286 + x = 0.327813567 Solving -0.01785714286 + x = 0.327813567 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01785714286' to each side of the equation. -0.01785714286 + 0.01785714286 + x = 0.327813567 + 0.01785714286 Combine like terms: -0.01785714286 + 0.01785714286 = 0.00000000000 0.00000000000 + x = 0.327813567 + 0.01785714286 x = 0.327813567 + 0.01785714286 Combine like terms: 0.327813567 + 0.01785714286 = 0.34567070986 x = 0.34567070986 Simplifying x = 0.34567070986Subproblem 2
x + -0.01785714286 = -0.327813567 Simplifying x + -0.01785714286 = -0.327813567 Reorder the terms: -0.01785714286 + x = -0.327813567 Solving -0.01785714286 + x = -0.327813567 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01785714286' to each side of the equation. -0.01785714286 + 0.01785714286 + x = -0.327813567 + 0.01785714286 Combine like terms: -0.01785714286 + 0.01785714286 = 0.00000000000 0.00000000000 + x = -0.327813567 + 0.01785714286 x = -0.327813567 + 0.01785714286 Combine like terms: -0.327813567 + 0.01785714286 = -0.30995642414 x = -0.30995642414 Simplifying x = -0.30995642414Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.34567070986, -0.30995642414}Solution
x = {0.34567070986, -0.30995642414}
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