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Simplifying 7z2 + -2z + -1 = 0 Reorder the terms: -1 + -2z + 7z2 = 0 Solving -1 + -2z + 7z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -0.2857142857z + z2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -0.2857142857z + 0.1428571429 + z2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -0.2857142857z + z2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -0.2857142857z + z2 = 0 + 0.1428571429 -0.2857142857z + z2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -0.2857142857z + z2 = 0.1428571429 The z term is -0.2857142857z. 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. -0.2857142857z + 0.02040816328 + z2 = 0.1428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857z + z2 = 0.1428571429 + 0.02040816328 Combine like terms: 0.1428571429 + 0.02040816328 = 0.16326530618 0.02040816328 + -0.2857142857z + z2 = 0.16326530618 Factor a perfect square on the left side: (z + -0.1428571429)(z + -0.1428571429) = 0.16326530618 Calculate the square root of the right side: 0.404061018 Break this problem into two subproblems by setting (z + -0.1428571429) equal to 0.404061018 and -0.404061018.Subproblem 1
z + -0.1428571429 = 0.404061018 Simplifying z + -0.1428571429 = 0.404061018 Reorder the terms: -0.1428571429 + z = 0.404061018 Solving -0.1428571429 + z = 0.404061018 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + z = 0.404061018 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + z = 0.404061018 + 0.1428571429 z = 0.404061018 + 0.1428571429 Combine like terms: 0.404061018 + 0.1428571429 = 0.5469181609 z = 0.5469181609 Simplifying z = 0.5469181609Subproblem 2
z + -0.1428571429 = -0.404061018 Simplifying z + -0.1428571429 = -0.404061018 Reorder the terms: -0.1428571429 + z = -0.404061018 Solving -0.1428571429 + z = -0.404061018 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + z = -0.404061018 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + z = -0.404061018 + 0.1428571429 z = -0.404061018 + 0.1428571429 Combine like terms: -0.404061018 + 0.1428571429 = -0.2612038751 z = -0.2612038751 Simplifying z = -0.2612038751Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.5469181609, -0.2612038751}
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