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Simplifying -1[5z(13z + 2)] = 2 + (7z + 6) Reorder the terms: -1[5z(2 + 13z)] = 2 + (7z + 6) -1[(2 * 5z + 13z * 5z)] = 2 + (7z + 6) -1[(10z + 65z2)] = 2 + (7z + 6) [10z * -1 + 65z2 * -1] = 2 + (7z + 6) [-10z + -65z2] = 2 + (7z + 6) Reorder the terms: -10z + -65z2 = 2 + (6 + 7z) Remove parenthesis around (6 + 7z) -10z + -65z2 = 2 + 6 + 7z Combine like terms: 2 + 6 = 8 -10z + -65z2 = 8 + 7z Solving -10z + -65z2 = 8 + 7z Solving for variable 'z'. Reorder the terms: -8 + -10z + -7z + -65z2 = 8 + 7z + -8 + -7z Combine like terms: -10z + -7z = -17z -8 + -17z + -65z2 = 8 + 7z + -8 + -7z Reorder the terms: -8 + -17z + -65z2 = 8 + -8 + 7z + -7z Combine like terms: 8 + -8 = 0 -8 + -17z + -65z2 = 0 + 7z + -7z -8 + -17z + -65z2 = 7z + -7z Combine like terms: 7z + -7z = 0 -8 + -17z + -65z2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 17z + 65z2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 17z + 65z2)' equal to zero and attempt to solve: Simplifying 8 + 17z + 65z2 = 0 Solving 8 + 17z + 65z2 = 0 Begin completing the square. Divide all terms by 65 the coefficient of the squared term: Divide each side by '65'. 0.1230769231 + 0.2615384615z + z2 = 0 Move the constant term to the right: Add '-0.1230769231' to each side of the equation. 0.1230769231 + 0.2615384615z + -0.1230769231 + z2 = 0 + -0.1230769231 Reorder the terms: 0.1230769231 + -0.1230769231 + 0.2615384615z + z2 = 0 + -0.1230769231 Combine like terms: 0.1230769231 + -0.1230769231 = 0.0000000000 0.0000000000 + 0.2615384615z + z2 = 0 + -0.1230769231 0.2615384615z + z2 = 0 + -0.1230769231 Combine like terms: 0 + -0.1230769231 = -0.1230769231 0.2615384615z + z2 = -0.1230769231 The z term is 0.2615384615z. Take half its coefficient (0.1307692308). Square it (0.01710059172) and add it to both sides. Add '0.01710059172' to each side of the equation. 0.2615384615z + 0.01710059172 + z2 = -0.1230769231 + 0.01710059172 Reorder the terms: 0.01710059172 + 0.2615384615z + z2 = -0.1230769231 + 0.01710059172 Combine like terms: -0.1230769231 + 0.01710059172 = -0.10597633138 0.01710059172 + 0.2615384615z + z2 = -0.10597633138 Factor a perfect square on the left side: (z + 0.1307692308)(z + 0.1307692308) = -0.10597633138 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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