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Simplifying z2 + -20z = -15 Reorder the terms: -20z + z2 = -15 Solving -20z + z2 = -15 Solving for variable 'z'. Reorder the terms: 15 + -20z + z2 = -15 + 15 Combine like terms: -15 + 15 = 0 15 + -20z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -20z + -15 + z2 = 0 + -15 Reorder the terms: 15 + -15 + -20z + z2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -20z + z2 = 0 + -15 -20z + z2 = 0 + -15 Combine like terms: 0 + -15 = -15 -20z + z2 = -15 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 = -15 + 100 Reorder the terms: 100 + -20z + z2 = -15 + 100 Combine like terms: -15 + 100 = 85 100 + -20z + z2 = 85 Factor a perfect square on the left side: (z + -10)(z + -10) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (z + -10) equal to 9.219544457 and -9.219544457.Subproblem 1
z + -10 = 9.219544457 Simplifying z + -10 = 9.219544457 Reorder the terms: -10 + z = 9.219544457 Solving -10 + z = 9.219544457 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 = 9.219544457 + 10 Combine like terms: -10 + 10 = 0 0 + z = 9.219544457 + 10 z = 9.219544457 + 10 Combine like terms: 9.219544457 + 10 = 19.219544457 z = 19.219544457 Simplifying z = 19.219544457Subproblem 2
z + -10 = -9.219544457 Simplifying z + -10 = -9.219544457 Reorder the terms: -10 + z = -9.219544457 Solving -10 + z = -9.219544457 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 = -9.219544457 + 10 Combine like terms: -10 + 10 = 0 0 + z = -9.219544457 + 10 z = -9.219544457 + 10 Combine like terms: -9.219544457 + 10 = 0.780455543 z = 0.780455543 Simplifying z = 0.780455543Solution
The solution to the problem is based on the solutions from the subproblems. z = {19.219544457, 0.780455543}
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