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Simplifying 7z + -10 = z2 + -7z + 2 Reorder the terms: -10 + 7z = z2 + -7z + 2 Reorder the terms: -10 + 7z = 2 + -7z + z2 Solving -10 + 7z = 2 + -7z + z2 Solving for variable 'z'. Reorder the terms: -10 + -2 + 7z + 7z + -1z2 = 2 + -7z + z2 + -2 + 7z + -1z2 Combine like terms: -10 + -2 = -12 -12 + 7z + 7z + -1z2 = 2 + -7z + z2 + -2 + 7z + -1z2 Combine like terms: 7z + 7z = 14z -12 + 14z + -1z2 = 2 + -7z + z2 + -2 + 7z + -1z2 Reorder the terms: -12 + 14z + -1z2 = 2 + -2 + -7z + 7z + z2 + -1z2 Combine like terms: 2 + -2 = 0 -12 + 14z + -1z2 = 0 + -7z + 7z + z2 + -1z2 -12 + 14z + -1z2 = -7z + 7z + z2 + -1z2 Combine like terms: -7z + 7z = 0 -12 + 14z + -1z2 = 0 + z2 + -1z2 -12 + 14z + -1z2 = z2 + -1z2 Combine like terms: z2 + -1z2 = 0 -12 + 14z + -1z2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12 + -14z + z2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -14z + -12 + z2 = 0 + -12 Reorder the terms: 12 + -12 + -14z + z2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -14z + z2 = 0 + -12 -14z + z2 = 0 + -12 Combine like terms: 0 + -12 = -12 -14z + z2 = -12 The z term is -14z. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14z + 49 + z2 = -12 + 49 Reorder the terms: 49 + -14z + z2 = -12 + 49 Combine like terms: -12 + 49 = 37 49 + -14z + z2 = 37 Factor a perfect square on the left side: (z + -7)(z + -7) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (z + -7) equal to 6.08276253 and -6.08276253.Subproblem 1
z + -7 = 6.08276253 Simplifying z + -7 = 6.08276253 Reorder the terms: -7 + z = 6.08276253 Solving -7 + z = 6.08276253 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + z = 6.08276253 + 7 Combine like terms: -7 + 7 = 0 0 + z = 6.08276253 + 7 z = 6.08276253 + 7 Combine like terms: 6.08276253 + 7 = 13.08276253 z = 13.08276253 Simplifying z = 13.08276253Subproblem 2
z + -7 = -6.08276253 Simplifying z + -7 = -6.08276253 Reorder the terms: -7 + z = -6.08276253 Solving -7 + z = -6.08276253 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + z = -6.08276253 + 7 Combine like terms: -7 + 7 = 0 0 + z = -6.08276253 + 7 z = -6.08276253 + 7 Combine like terms: -6.08276253 + 7 = 0.91723747 z = 0.91723747 Simplifying z = 0.91723747Solution
The solution to the problem is based on the solutions from the subproblems. z = {13.08276253, 0.91723747}
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