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Simplifying z2 + -7z + -3 = 0 Reorder the terms: -3 + -7z + z2 = 0 Solving -3 + -7z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -7z + 3 + z2 = 0 + 3 Reorder the terms: -3 + 3 + -7z + z2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7z + z2 = 0 + 3 -7z + z2 = 0 + 3 Combine like terms: 0 + 3 = 3 -7z + z2 = 3 The z term is -7z. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7z + 12.25 + z2 = 3 + 12.25 Reorder the terms: 12.25 + -7z + z2 = 3 + 12.25 Combine like terms: 3 + 12.25 = 15.25 12.25 + -7z + z2 = 15.25 Factor a perfect square on the left side: (z + -3.5)(z + -3.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (z + -3.5) equal to 3.905124838 and -3.905124838.Subproblem 1
z + -3.5 = 3.905124838 Simplifying z + -3.5 = 3.905124838 Reorder the terms: -3.5 + z = 3.905124838 Solving -3.5 + z = 3.905124838 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + z = 3.905124838 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + z = 3.905124838 + 3.5 z = 3.905124838 + 3.5 Combine like terms: 3.905124838 + 3.5 = 7.405124838 z = 7.405124838 Simplifying z = 7.405124838Subproblem 2
z + -3.5 = -3.905124838 Simplifying z + -3.5 = -3.905124838 Reorder the terms: -3.5 + z = -3.905124838 Solving -3.5 + z = -3.905124838 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + z = -3.905124838 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + z = -3.905124838 + 3.5 z = -3.905124838 + 3.5 Combine like terms: -3.905124838 + 3.5 = -0.405124838 z = -0.405124838 Simplifying z = -0.405124838Solution
The solution to the problem is based on the solutions from the subproblems. z = {7.405124838, -0.405124838}
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