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Simplifying (5z2 + 3z + -5) + -1(6z2 + -7z + -9) = 0 Reorder the terms: (-5 + 3z + 5z2) + -1(6z2 + -7z + -9) = 0 Remove parenthesis around (-5 + 3z + 5z2) -5 + 3z + 5z2 + -1(6z2 + -7z + -9) = 0 Reorder the terms: -5 + 3z + 5z2 + -1(-9 + -7z + 6z2) = 0 -5 + 3z + 5z2 + (-9 * -1 + -7z * -1 + 6z2 * -1) = 0 -5 + 3z + 5z2 + (9 + 7z + -6z2) = 0 Reorder the terms: -5 + 9 + 3z + 7z + 5z2 + -6z2 = 0 Combine like terms: -5 + 9 = 4 4 + 3z + 7z + 5z2 + -6z2 = 0 Combine like terms: 3z + 7z = 10z 4 + 10z + 5z2 + -6z2 = 0 Combine like terms: 5z2 + -6z2 = -1z2 4 + 10z + -1z2 = 0 Solving 4 + 10z + -1z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -10z + z2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -10z + 4 + z2 = 0 + 4 Reorder the terms: -4 + 4 + -10z + z2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -10z + z2 = 0 + 4 -10z + z2 = 0 + 4 Combine like terms: 0 + 4 = 4 -10z + z2 = 4 The z term is -10z. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10z + 25 + z2 = 4 + 25 Reorder the terms: 25 + -10z + z2 = 4 + 25 Combine like terms: 4 + 25 = 29 25 + -10z + z2 = 29 Factor a perfect square on the left side: (z + -5)(z + -5) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (z + -5) equal to 5.385164807 and -5.385164807.Subproblem 1
z + -5 = 5.385164807 Simplifying z + -5 = 5.385164807 Reorder the terms: -5 + z = 5.385164807 Solving -5 + z = 5.385164807 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = 5.385164807 + 5 Combine like terms: -5 + 5 = 0 0 + z = 5.385164807 + 5 z = 5.385164807 + 5 Combine like terms: 5.385164807 + 5 = 10.385164807 z = 10.385164807 Simplifying z = 10.385164807Subproblem 2
z + -5 = -5.385164807 Simplifying z + -5 = -5.385164807 Reorder the terms: -5 + z = -5.385164807 Solving -5 + z = -5.385164807 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = -5.385164807 + 5 Combine like terms: -5 + 5 = 0 0 + z = -5.385164807 + 5 z = -5.385164807 + 5 Combine like terms: -5.385164807 + 5 = -0.385164807 z = -0.385164807 Simplifying z = -0.385164807Solution
The solution to the problem is based on the solutions from the subproblems. z = {10.385164807, -0.385164807}
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