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Simplifying 21x2 + -6x + -3 = 0 Reorder the terms: -3 + -6x + 21x2 = 0 Solving -3 + -6x + 21x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -2x + 7x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -2x + 7x2)' equal to zero and attempt to solve: Simplifying -1 + -2x + 7x2 = 0 Solving -1 + -2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -0.2857142857x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -0.2857142857x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -0.2857142857x + x2 = 0 + 0.1428571429 -0.2857142857x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -0.2857142857x + x2 = 0.1428571429 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = 0.1428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 0.1428571429 + 0.02040816328 Combine like terms: 0.1428571429 + 0.02040816328 = 0.16326530618 0.02040816328 + -0.2857142857x + x2 = 0.16326530618 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 0.16326530618 Calculate the square root of the right side: 0.404061018 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 0.404061018 and -0.404061018.Subproblem 1
x + -0.1428571429 = 0.404061018 Simplifying x + -0.1428571429 = 0.404061018 Reorder the terms: -0.1428571429 + x = 0.404061018 Solving -0.1428571429 + x = 0.404061018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 0.404061018 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 0.404061018 + 0.1428571429 x = 0.404061018 + 0.1428571429 Combine like terms: 0.404061018 + 0.1428571429 = 0.5469181609 x = 0.5469181609 Simplifying x = 0.5469181609Subproblem 2
x + -0.1428571429 = -0.404061018 Simplifying x + -0.1428571429 = -0.404061018 Reorder the terms: -0.1428571429 + x = -0.404061018 Solving -0.1428571429 + x = -0.404061018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -0.404061018 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -0.404061018 + 0.1428571429 x = -0.404061018 + 0.1428571429 Combine like terms: -0.404061018 + 0.1428571429 = -0.2612038751 x = -0.2612038751 Simplifying x = -0.2612038751Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5469181609, -0.2612038751}Solution
x = {0.5469181609, -0.2612038751}
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