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Simplifying 4x2 + -68x + -6 = 0 Reorder the terms: -6 + -68x + 4x2 = 0 Solving -6 + -68x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -34x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -34x + 2x2)' equal to zero and attempt to solve: Simplifying -3 + -34x + 2x2 = 0 Solving -3 + -34x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -17x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -17x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -17x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -17x + x2 = 0 + 1.5 -17x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -17x + x2 = 1.5 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = 1.5 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 1.5 + 72.25 Combine like terms: 1.5 + 72.25 = 73.75 72.25 + -17x + x2 = 73.75 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 73.75 Calculate the square root of the right side: 8.587782019 Break this problem into two subproblems by setting (x + -8.5) equal to 8.587782019 and -8.587782019.Subproblem 1
x + -8.5 = 8.587782019 Simplifying x + -8.5 = 8.587782019 Reorder the terms: -8.5 + x = 8.587782019 Solving -8.5 + x = 8.587782019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 8.587782019 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 8.587782019 + 8.5 x = 8.587782019 + 8.5 Combine like terms: 8.587782019 + 8.5 = 17.087782019 x = 17.087782019 Simplifying x = 17.087782019Subproblem 2
x + -8.5 = -8.587782019 Simplifying x + -8.5 = -8.587782019 Reorder the terms: -8.5 + x = -8.587782019 Solving -8.5 + x = -8.587782019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -8.587782019 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -8.587782019 + 8.5 x = -8.587782019 + 8.5 Combine like terms: -8.587782019 + 8.5 = -0.087782019 x = -0.087782019 Simplifying x = -0.087782019Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.087782019, -0.087782019}Solution
x = {17.087782019, -0.087782019}
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