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Simplifying z2 + 20z + -43 = 0 Reorder the terms: -43 + 20z + z2 = 0 Solving -43 + 20z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 20z + 43 + z2 = 0 + 43 Reorder the terms: -43 + 43 + 20z + z2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 20z + z2 = 0 + 43 20z + z2 = 0 + 43 Combine like terms: 0 + 43 = 43 20z + z2 = 43 The z term is 20z. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20z + 100 + z2 = 43 + 100 Reorder the terms: 100 + 20z + z2 = 43 + 100 Combine like terms: 43 + 100 = 143 100 + 20z + z2 = 143 Factor a perfect square on the left side: (z + 10)(z + 10) = 143 Calculate the square root of the right side: 11.958260743 Break this problem into two subproblems by setting (z + 10) equal to 11.958260743 and -11.958260743.Subproblem 1
z + 10 = 11.958260743 Simplifying z + 10 = 11.958260743 Reorder the terms: 10 + z = 11.958260743 Solving 10 + z = 11.958260743 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + z = 11.958260743 + -10 Combine like terms: 10 + -10 = 0 0 + z = 11.958260743 + -10 z = 11.958260743 + -10 Combine like terms: 11.958260743 + -10 = 1.958260743 z = 1.958260743 Simplifying z = 1.958260743Subproblem 2
z + 10 = -11.958260743 Simplifying z + 10 = -11.958260743 Reorder the terms: 10 + z = -11.958260743 Solving 10 + z = -11.958260743 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + z = -11.958260743 + -10 Combine like terms: 10 + -10 = 0 0 + z = -11.958260743 + -10 z = -11.958260743 + -10 Combine like terms: -11.958260743 + -10 = -21.958260743 z = -21.958260743 Simplifying z = -21.958260743Solution
The solution to the problem is based on the solutions from the subproblems. z = {1.958260743, -21.958260743}
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