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Simplifying 9z2 + 10z + -4 = 0 Reorder the terms: -4 + 10z + 9z2 = 0 Solving -4 + 10z + 9z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + 1.111111111z + z2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 1.111111111z + 0.4444444444 + z2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 1.111111111z + z2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 1.111111111z + z2 = 0 + 0.4444444444 1.111111111z + z2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 1.111111111z + z2 = 0.4444444444 The z term is 1.111111111z. Take half its coefficient (0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. 1.111111111z + 0.3086419752 + z2 = 0.4444444444 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111z + z2 = 0.4444444444 + 0.3086419752 Combine like terms: 0.4444444444 + 0.3086419752 = 0.7530864196 0.3086419752 + 1.111111111z + z2 = 0.7530864196 Factor a perfect square on the left side: (z + 0.5555555555)(z + 0.5555555555) = 0.7530864196 Calculate the square root of the right side: 0.867805519 Break this problem into two subproblems by setting (z + 0.5555555555) equal to 0.867805519 and -0.867805519.Subproblem 1
z + 0.5555555555 = 0.867805519 Simplifying z + 0.5555555555 = 0.867805519 Reorder the terms: 0.5555555555 + z = 0.867805519 Solving 0.5555555555 + z = 0.867805519 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + z = 0.867805519 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + z = 0.867805519 + -0.5555555555 z = 0.867805519 + -0.5555555555 Combine like terms: 0.867805519 + -0.5555555555 = 0.3122499635 z = 0.3122499635 Simplifying z = 0.3122499635Subproblem 2
z + 0.5555555555 = -0.867805519 Simplifying z + 0.5555555555 = -0.867805519 Reorder the terms: 0.5555555555 + z = -0.867805519 Solving 0.5555555555 + z = -0.867805519 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + z = -0.867805519 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + z = -0.867805519 + -0.5555555555 z = -0.867805519 + -0.5555555555 Combine like terms: -0.867805519 + -0.5555555555 = -1.4233610745 z = -1.4233610745 Simplifying z = -1.4233610745Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.3122499635, -1.4233610745}
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