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Simplifying 21z2 + 8z + -26 = 0 Reorder the terms: -26 + 8z + 21z2 = 0 Solving -26 + 8z + 21z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -1.238095238 + 0.380952381z + z2 = 0 Move the constant term to the right: Add '1.238095238' to each side of the equation. -1.238095238 + 0.380952381z + 1.238095238 + z2 = 0 + 1.238095238 Reorder the terms: -1.238095238 + 1.238095238 + 0.380952381z + z2 = 0 + 1.238095238 Combine like terms: -1.238095238 + 1.238095238 = 0.000000000 0.000000000 + 0.380952381z + z2 = 0 + 1.238095238 0.380952381z + z2 = 0 + 1.238095238 Combine like terms: 0 + 1.238095238 = 1.238095238 0.380952381z + z2 = 1.238095238 The z term is 0.380952381z. Take half its coefficient (0.1904761905). Square it (0.03628117915) and add it to both sides. Add '0.03628117915' to each side of the equation. 0.380952381z + 0.03628117915 + z2 = 1.238095238 + 0.03628117915 Reorder the terms: 0.03628117915 + 0.380952381z + z2 = 1.238095238 + 0.03628117915 Combine like terms: 1.238095238 + 0.03628117915 = 1.27437641715 0.03628117915 + 0.380952381z + z2 = 1.27437641715 Factor a perfect square on the left side: (z + 0.1904761905)(z + 0.1904761905) = 1.27437641715 Calculate the square root of the right side: 1.128882818 Break this problem into two subproblems by setting (z + 0.1904761905) equal to 1.128882818 and -1.128882818.Subproblem 1
z + 0.1904761905 = 1.128882818 Simplifying z + 0.1904761905 = 1.128882818 Reorder the terms: 0.1904761905 + z = 1.128882818 Solving 0.1904761905 + z = 1.128882818 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.1904761905' to each side of the equation. 0.1904761905 + -0.1904761905 + z = 1.128882818 + -0.1904761905 Combine like terms: 0.1904761905 + -0.1904761905 = 0.0000000000 0.0000000000 + z = 1.128882818 + -0.1904761905 z = 1.128882818 + -0.1904761905 Combine like terms: 1.128882818 + -0.1904761905 = 0.9384066275 z = 0.9384066275 Simplifying z = 0.9384066275Subproblem 2
z + 0.1904761905 = -1.128882818 Simplifying z + 0.1904761905 = -1.128882818 Reorder the terms: 0.1904761905 + z = -1.128882818 Solving 0.1904761905 + z = -1.128882818 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.1904761905' to each side of the equation. 0.1904761905 + -0.1904761905 + z = -1.128882818 + -0.1904761905 Combine like terms: 0.1904761905 + -0.1904761905 = 0.0000000000 0.0000000000 + z = -1.128882818 + -0.1904761905 z = -1.128882818 + -0.1904761905 Combine like terms: -1.128882818 + -0.1904761905 = -1.3193590085 z = -1.3193590085 Simplifying z = -1.3193590085Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.9384066275, -1.3193590085}
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