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Simplifying 25z2 + 93 = 100z Reorder the terms: 93 + 25z2 = 100z Solving 93 + 25z2 = 100z Solving for variable 'z'. Reorder the terms: 93 + -100z + 25z2 = 100z + -100z Combine like terms: 100z + -100z = 0 93 + -100z + 25z2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 3.72 + -4z + z2 = 0 Move the constant term to the right: Add '-3.72' to each side of the equation. 3.72 + -4z + -3.72 + z2 = 0 + -3.72 Reorder the terms: 3.72 + -3.72 + -4z + z2 = 0 + -3.72 Combine like terms: 3.72 + -3.72 = 0.00 0.00 + -4z + z2 = 0 + -3.72 -4z + z2 = 0 + -3.72 Combine like terms: 0 + -3.72 = -3.72 -4z + z2 = -3.72 The z term is -4z. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4z + 4 + z2 = -3.72 + 4 Reorder the terms: 4 + -4z + z2 = -3.72 + 4 Combine like terms: -3.72 + 4 = 0.28 4 + -4z + z2 = 0.28 Factor a perfect square on the left side: (z + -2)(z + -2) = 0.28 Calculate the square root of the right side: 0.529150262 Break this problem into two subproblems by setting (z + -2) equal to 0.529150262 and -0.529150262.Subproblem 1
z + -2 = 0.529150262 Simplifying z + -2 = 0.529150262 Reorder the terms: -2 + z = 0.529150262 Solving -2 + z = 0.529150262 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = 0.529150262 + 2 Combine like terms: -2 + 2 = 0 0 + z = 0.529150262 + 2 z = 0.529150262 + 2 Combine like terms: 0.529150262 + 2 = 2.529150262 z = 2.529150262 Simplifying z = 2.529150262Subproblem 2
z + -2 = -0.529150262 Simplifying z + -2 = -0.529150262 Reorder the terms: -2 + z = -0.529150262 Solving -2 + z = -0.529150262 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = -0.529150262 + 2 Combine like terms: -2 + 2 = 0 0 + z = -0.529150262 + 2 z = -0.529150262 + 2 Combine like terms: -0.529150262 + 2 = 1.470849738 z = 1.470849738 Simplifying z = 1.470849738Solution
The solution to the problem is based on the solutions from the subproblems. z = {2.529150262, 1.470849738}
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