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Simplifying 34x2 + 4x + -6 = 10 Reorder the terms: -6 + 4x + 34x2 = 10 Solving -6 + 4x + 34x2 = 10 Solving for variable 'x'. Reorder the terms: -6 + -10 + 4x + 34x2 = 10 + -10 Combine like terms: -6 + -10 = -16 -16 + 4x + 34x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -16 + 4x + 34x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 2x + 17x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 2x + 17x2)' equal to zero and attempt to solve: Simplifying -8 + 2x + 17x2 = 0 Solving -8 + 2x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.4705882353 + 0.1176470588x + x2 = 0 Move the constant term to the right: Add '0.4705882353' to each side of the equation. -0.4705882353 + 0.1176470588x + 0.4705882353 + x2 = 0 + 0.4705882353 Reorder the terms: -0.4705882353 + 0.4705882353 + 0.1176470588x + x2 = 0 + 0.4705882353 Combine like terms: -0.4705882353 + 0.4705882353 = 0.0000000000 0.0000000000 + 0.1176470588x + x2 = 0 + 0.4705882353 0.1176470588x + x2 = 0 + 0.4705882353 Combine like terms: 0 + 0.4705882353 = 0.4705882353 0.1176470588x + x2 = 0.4705882353 The x term is 0.1176470588x. Take half its coefficient (0.0588235294). Square it (0.003460207611) and add it to both sides. Add '0.003460207611' to each side of the equation. 0.1176470588x + 0.003460207611 + x2 = 0.4705882353 + 0.003460207611 Reorder the terms: 0.003460207611 + 0.1176470588x + x2 = 0.4705882353 + 0.003460207611 Combine like terms: 0.4705882353 + 0.003460207611 = 0.474048442911 0.003460207611 + 0.1176470588x + x2 = 0.474048442911 Factor a perfect square on the left side: (x + 0.0588235294)(x + 0.0588235294) = 0.474048442911 Calculate the square root of the right side: 0.688511759 Break this problem into two subproblems by setting (x + 0.0588235294) equal to 0.688511759 and -0.688511759.Subproblem 1
x + 0.0588235294 = 0.688511759 Simplifying x + 0.0588235294 = 0.688511759 Reorder the terms: 0.0588235294 + x = 0.688511759 Solving 0.0588235294 + x = 0.688511759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0588235294' to each side of the equation. 0.0588235294 + -0.0588235294 + x = 0.688511759 + -0.0588235294 Combine like terms: 0.0588235294 + -0.0588235294 = 0.0000000000 0.0000000000 + x = 0.688511759 + -0.0588235294 x = 0.688511759 + -0.0588235294 Combine like terms: 0.688511759 + -0.0588235294 = 0.6296882296 x = 0.6296882296 Simplifying x = 0.6296882296Subproblem 2
x + 0.0588235294 = -0.688511759 Simplifying x + 0.0588235294 = -0.688511759 Reorder the terms: 0.0588235294 + x = -0.688511759 Solving 0.0588235294 + x = -0.688511759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0588235294' to each side of the equation. 0.0588235294 + -0.0588235294 + x = -0.688511759 + -0.0588235294 Combine like terms: 0.0588235294 + -0.0588235294 = 0.0000000000 0.0000000000 + x = -0.688511759 + -0.0588235294 x = -0.688511759 + -0.0588235294 Combine like terms: -0.688511759 + -0.0588235294 = -0.7473352884 x = -0.7473352884 Simplifying x = -0.7473352884Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6296882296, -0.7473352884}Solution
x = {0.6296882296, -0.7473352884}
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