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Simplifying 2z7 + 7z6 = 5z5 Reorder the terms: 7z6 + 2z7 = 5z5 Solving 7z6 + 2z7 = 5z5 Solving for variable 'z'. Reorder the terms: -5z5 + 7z6 + 2z7 = 5z5 + -5z5 Combine like terms: 5z5 + -5z5 = 0 -5z5 + 7z6 + 2z7 = 0 Factor out the Greatest Common Factor (GCF), 'z5'. z5(-5 + 7z + 2z2) = 0Subproblem 1
Set the factor 'z5' equal to zero and attempt to solve: Simplifying z5 = 0 Solving z5 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z5 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-5 + 7z + 2z2)' equal to zero and attempt to solve: Simplifying -5 + 7z + 2z2 = 0 Solving -5 + 7z + 2z2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 3.5z + z2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 3.5z + 2.5 + z2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 3.5z + z2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 3.5z + z2 = 0 + 2.5 3.5z + z2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 3.5z + z2 = 2.5 The z term is 3.5z. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5z + 3.0625 + z2 = 2.5 + 3.0625 Reorder the terms: 3.0625 + 3.5z + z2 = 2.5 + 3.0625 Combine like terms: 2.5 + 3.0625 = 5.5625 3.0625 + 3.5z + z2 = 5.5625 Factor a perfect square on the left side: (z + 1.75)(z + 1.75) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (z + 1.75) equal to 2.358495283 and -2.358495283.Subproblem 1
z + 1.75 = 2.358495283 Simplifying z + 1.75 = 2.358495283 Reorder the terms: 1.75 + z = 2.358495283 Solving 1.75 + z = 2.358495283 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + z = 2.358495283 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + z = 2.358495283 + -1.75 z = 2.358495283 + -1.75 Combine like terms: 2.358495283 + -1.75 = 0.608495283 z = 0.608495283 Simplifying z = 0.608495283Subproblem 2
z + 1.75 = -2.358495283 Simplifying z + 1.75 = -2.358495283 Reorder the terms: 1.75 + z = -2.358495283 Solving 1.75 + z = -2.358495283 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + z = -2.358495283 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + z = -2.358495283 + -1.75 z = -2.358495283 + -1.75 Combine like terms: -2.358495283 + -1.75 = -4.108495283 z = -4.108495283 Simplifying z = -4.108495283Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.608495283, -4.108495283}Solution
z = {0.608495283, -4.108495283}
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