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Simplifying 5z2 + -17z = 14 Reorder the terms: -17z + 5z2 = 14 Solving -17z + 5z2 = 14 Solving for variable 'z'. Reorder the terms: -14 + -17z + 5z2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -17z + 5z2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + -3.4z + z2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -3.4z + 2.8 + z2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + -3.4z + z2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -3.4z + z2 = 0 + 2.8 -3.4z + z2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 -3.4z + z2 = 2.8 The z term is -3.4z. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4z + 2.89 + z2 = 2.8 + 2.89 Reorder the terms: 2.89 + -3.4z + z2 = 2.8 + 2.89 Combine like terms: 2.8 + 2.89 = 5.69 2.89 + -3.4z + z2 = 5.69 Factor a perfect square on the left side: (z + -1.7)(z + -1.7) = 5.69 Calculate the square root of the right side: 2.385372088 Break this problem into two subproblems by setting (z + -1.7) equal to 2.385372088 and -2.385372088.Subproblem 1
z + -1.7 = 2.385372088 Simplifying z + -1.7 = 2.385372088 Reorder the terms: -1.7 + z = 2.385372088 Solving -1.7 + z = 2.385372088 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + z = 2.385372088 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + z = 2.385372088 + 1.7 z = 2.385372088 + 1.7 Combine like terms: 2.385372088 + 1.7 = 4.085372088 z = 4.085372088 Simplifying z = 4.085372088Subproblem 2
z + -1.7 = -2.385372088 Simplifying z + -1.7 = -2.385372088 Reorder the terms: -1.7 + z = -2.385372088 Solving -1.7 + z = -2.385372088 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + z = -2.385372088 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + z = -2.385372088 + 1.7 z = -2.385372088 + 1.7 Combine like terms: -2.385372088 + 1.7 = -0.685372088 z = -0.685372088 Simplifying z = -0.685372088Solution
The solution to the problem is based on the solutions from the subproblems. z = {4.085372088, -0.685372088}
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