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Simplifying 42x2 + -34x + -6 = 0 Reorder the terms: -6 + -34x + 42x2 = 0 Solving -6 + -34x + 42x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -17x + 21x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -17x + 21x2)' equal to zero and attempt to solve: Simplifying -3 + -17x + 21x2 = 0 Solving -3 + -17x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.1428571429 + -0.8095238095x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -0.8095238095x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -0.8095238095x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -0.8095238095x + x2 = 0 + 0.1428571429 -0.8095238095x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -0.8095238095x + x2 = 0.1428571429 The x term is -0.8095238095x. Take half its coefficient (-0.4047619048). Square it (0.1638321996) and add it to both sides. Add '0.1638321996' to each side of the equation. -0.8095238095x + 0.1638321996 + x2 = 0.1428571429 + 0.1638321996 Reorder the terms: 0.1638321996 + -0.8095238095x + x2 = 0.1428571429 + 0.1638321996 Combine like terms: 0.1428571429 + 0.1638321996 = 0.3066893425 0.1638321996 + -0.8095238095x + x2 = 0.3066893425 Factor a perfect square on the left side: (x + -0.4047619048)(x + -0.4047619048) = 0.3066893425 Calculate the square root of the right side: 0.553795398 Break this problem into two subproblems by setting (x + -0.4047619048) equal to 0.553795398 and -0.553795398.Subproblem 1
x + -0.4047619048 = 0.553795398 Simplifying x + -0.4047619048 = 0.553795398 Reorder the terms: -0.4047619048 + x = 0.553795398 Solving -0.4047619048 + x = 0.553795398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4047619048' to each side of the equation. -0.4047619048 + 0.4047619048 + x = 0.553795398 + 0.4047619048 Combine like terms: -0.4047619048 + 0.4047619048 = 0.0000000000 0.0000000000 + x = 0.553795398 + 0.4047619048 x = 0.553795398 + 0.4047619048 Combine like terms: 0.553795398 + 0.4047619048 = 0.9585573028 x = 0.9585573028 Simplifying x = 0.9585573028Subproblem 2
x + -0.4047619048 = -0.553795398 Simplifying x + -0.4047619048 = -0.553795398 Reorder the terms: -0.4047619048 + x = -0.553795398 Solving -0.4047619048 + x = -0.553795398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4047619048' to each side of the equation. -0.4047619048 + 0.4047619048 + x = -0.553795398 + 0.4047619048 Combine like terms: -0.4047619048 + 0.4047619048 = 0.0000000000 0.0000000000 + x = -0.553795398 + 0.4047619048 x = -0.553795398 + 0.4047619048 Combine like terms: -0.553795398 + 0.4047619048 = -0.1490334932 x = -0.1490334932 Simplifying x = -0.1490334932Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9585573028, -0.1490334932}Solution
x = {0.9585573028, -0.1490334932}
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