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Simplifying z2 + 0.6z + -20.16 = 0 Reorder the terms: -20.16 + 0.6z + z2 = 0 Solving -20.16 + 0.6z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '20.16' to each side of the equation. -20.16 + 0.6z + 20.16 + z2 = 0 + 20.16 Reorder the terms: -20.16 + 20.16 + 0.6z + z2 = 0 + 20.16 Combine like terms: -20.16 + 20.16 = 0.00 0.00 + 0.6z + z2 = 0 + 20.16 0.6z + z2 = 0 + 20.16 Combine like terms: 0 + 20.16 = 20.16 0.6z + z2 = 20.16 The z term is 0.6z. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6z + 0.09 + z2 = 20.16 + 0.09 Reorder the terms: 0.09 + 0.6z + z2 = 20.16 + 0.09 Combine like terms: 20.16 + 0.09 = 20.25 0.09 + 0.6z + z2 = 20.25 Factor a perfect square on the left side: (z + 0.3)(z + 0.3) = 20.25 Calculate the square root of the right side: 4.5 Break this problem into two subproblems by setting (z + 0.3) equal to 4.5 and -4.5.Subproblem 1
z + 0.3 = 4.5 Simplifying z + 0.3 = 4.5 Reorder the terms: 0.3 + z = 4.5 Solving 0.3 + z = 4.5 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + z = 4.5 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + z = 4.5 + -0.3 z = 4.5 + -0.3 Combine like terms: 4.5 + -0.3 = 4.2 z = 4.2 Simplifying z = 4.2Subproblem 2
z + 0.3 = -4.5 Simplifying z + 0.3 = -4.5 Reorder the terms: 0.3 + z = -4.5 Solving 0.3 + z = -4.5 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + z = -4.5 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + z = -4.5 + -0.3 z = -4.5 + -0.3 Combine like terms: -4.5 + -0.3 = -4.8 z = -4.8 Simplifying z = -4.8Solution
The solution to the problem is based on the solutions from the subproblems. z = {4.2, -4.8}
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