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Simplifying 0 = z2 + -26z + 100 Reorder the terms: 0 = 100 + -26z + z2 Solving 0 = 100 + -26z + z2 Solving for variable 'z'. Combine like terms: 0 + -100 = -100 -100 + 26z + -1z2 = 100 + -26z + z2 + -100 + 26z + -1z2 Reorder the terms: -100 + 26z + -1z2 = 100 + -100 + -26z + 26z + z2 + -1z2 Combine like terms: 100 + -100 = 0 -100 + 26z + -1z2 = 0 + -26z + 26z + z2 + -1z2 -100 + 26z + -1z2 = -26z + 26z + z2 + -1z2 Combine like terms: -26z + 26z = 0 -100 + 26z + -1z2 = 0 + z2 + -1z2 -100 + 26z + -1z2 = z2 + -1z2 Combine like terms: z2 + -1z2 = 0 -100 + 26z + -1z2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 100 + -26z + z2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -26z + -100 + z2 = 0 + -100 Reorder the terms: 100 + -100 + -26z + z2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -26z + z2 = 0 + -100 -26z + z2 = 0 + -100 Combine like terms: 0 + -100 = -100 -26z + z2 = -100 The z term is -26z. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26z + 169 + z2 = -100 + 169 Reorder the terms: 169 + -26z + z2 = -100 + 169 Combine like terms: -100 + 169 = 69 169 + -26z + z2 = 69 Factor a perfect square on the left side: (z + -13)(z + -13) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (z + -13) equal to 8.306623863 and -8.306623863.Subproblem 1
z + -13 = 8.306623863 Simplifying z + -13 = 8.306623863 Reorder the terms: -13 + z = 8.306623863 Solving -13 + z = 8.306623863 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + z = 8.306623863 + 13 Combine like terms: -13 + 13 = 0 0 + z = 8.306623863 + 13 z = 8.306623863 + 13 Combine like terms: 8.306623863 + 13 = 21.306623863 z = 21.306623863 Simplifying z = 21.306623863Subproblem 2
z + -13 = -8.306623863 Simplifying z + -13 = -8.306623863 Reorder the terms: -13 + z = -8.306623863 Solving -13 + z = -8.306623863 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + z = -8.306623863 + 13 Combine like terms: -13 + 13 = 0 0 + z = -8.306623863 + 13 z = -8.306623863 + 13 Combine like terms: -8.306623863 + 13 = 4.693376137 z = 4.693376137 Simplifying z = 4.693376137Solution
The solution to the problem is based on the solutions from the subproblems. z = {21.306623863, 4.693376137}
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