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Simplifying z2 + -8z + 10 = 0 Reorder the terms: 10 + -8z + z2 = 0 Solving 10 + -8z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -8z + -10 + z2 = 0 + -10 Reorder the terms: 10 + -10 + -8z + z2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -8z + z2 = 0 + -10 -8z + z2 = 0 + -10 Combine like terms: 0 + -10 = -10 -8z + z2 = -10 The z term is -8z. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8z + 16 + z2 = -10 + 16 Reorder the terms: 16 + -8z + z2 = -10 + 16 Combine like terms: -10 + 16 = 6 16 + -8z + z2 = 6 Factor a perfect square on the left side: (z + -4)(z + -4) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (z + -4) equal to 2.449489743 and -2.449489743.Subproblem 1
z + -4 = 2.449489743 Simplifying z + -4 = 2.449489743 Reorder the terms: -4 + z = 2.449489743 Solving -4 + z = 2.449489743 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + z = 2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + z = 2.449489743 + 4 z = 2.449489743 + 4 Combine like terms: 2.449489743 + 4 = 6.449489743 z = 6.449489743 Simplifying z = 6.449489743Subproblem 2
z + -4 = -2.449489743 Simplifying z + -4 = -2.449489743 Reorder the terms: -4 + z = -2.449489743 Solving -4 + z = -2.449489743 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + z = -2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + z = -2.449489743 + 4 z = -2.449489743 + 4 Combine like terms: -2.449489743 + 4 = 1.550510257 z = 1.550510257 Simplifying z = 1.550510257Solution
The solution to the problem is based on the solutions from the subproblems. z = {6.449489743, 1.550510257}
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