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Simplifying z2 + -6z = 3 Reorder the terms: -6z + z2 = 3 Solving -6z + z2 = 3 Solving for variable 'z'. Reorder the terms: -3 + -6z + z2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -6z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -6z + 3 + z2 = 0 + 3 Reorder the terms: -3 + 3 + -6z + z2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -6z + z2 = 0 + 3 -6z + z2 = 0 + 3 Combine like terms: 0 + 3 = 3 -6z + z2 = 3 The z term is -6z. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6z + 9 + z2 = 3 + 9 Reorder the terms: 9 + -6z + z2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + -6z + z2 = 12 Factor a perfect square on the left side: (z + -3)(z + -3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (z + -3) equal to 3.464101615 and -3.464101615.Subproblem 1
z + -3 = 3.464101615 Simplifying z + -3 = 3.464101615 Reorder the terms: -3 + z = 3.464101615 Solving -3 + z = 3.464101615 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + z = 3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + z = 3.464101615 + 3 z = 3.464101615 + 3 Combine like terms: 3.464101615 + 3 = 6.464101615 z = 6.464101615 Simplifying z = 6.464101615Subproblem 2
z + -3 = -3.464101615 Simplifying z + -3 = -3.464101615 Reorder the terms: -3 + z = -3.464101615 Solving -3 + z = -3.464101615 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + z = -3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + z = -3.464101615 + 3 z = -3.464101615 + 3 Combine like terms: -3.464101615 + 3 = -0.464101615 z = -0.464101615 Simplifying z = -0.464101615Solution
The solution to the problem is based on the solutions from the subproblems. z = {6.464101615, -0.464101615}
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