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Simplifying z2 + -6z + -15 = 0 Reorder the terms: -15 + -6z + z2 = 0 Solving -15 + -6z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -6z + 15 + z2 = 0 + 15 Reorder the terms: -15 + 15 + -6z + z2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -6z + z2 = 0 + 15 -6z + z2 = 0 + 15 Combine like terms: 0 + 15 = 15 -6z + z2 = 15 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 = 15 + 9 Reorder the terms: 9 + -6z + z2 = 15 + 9 Combine like terms: 15 + 9 = 24 9 + -6z + z2 = 24 Factor a perfect square on the left side: (z + -3)(z + -3) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (z + -3) equal to 4.898979486 and -4.898979486.Subproblem 1
z + -3 = 4.898979486 Simplifying z + -3 = 4.898979486 Reorder the terms: -3 + z = 4.898979486 Solving -3 + z = 4.898979486 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 = 4.898979486 + 3 Combine like terms: -3 + 3 = 0 0 + z = 4.898979486 + 3 z = 4.898979486 + 3 Combine like terms: 4.898979486 + 3 = 7.898979486 z = 7.898979486 Simplifying z = 7.898979486Subproblem 2
z + -3 = -4.898979486 Simplifying z + -3 = -4.898979486 Reorder the terms: -3 + z = -4.898979486 Solving -3 + z = -4.898979486 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 = -4.898979486 + 3 Combine like terms: -3 + 3 = 0 0 + z = -4.898979486 + 3 z = -4.898979486 + 3 Combine like terms: -4.898979486 + 3 = -1.898979486 z = -1.898979486 Simplifying z = -1.898979486Solution
The solution to the problem is based on the solutions from the subproblems. z = {7.898979486, -1.898979486}
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