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Simplifying 3z2 + 95z + 12 = 0 Reorder the terms: 12 + 95z + 3z2 = 0 Solving 12 + 95z + 3z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + 31.66666667z + z2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 31.66666667z + -4 + z2 = 0 + -4 Reorder the terms: 4 + -4 + 31.66666667z + z2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 31.66666667z + z2 = 0 + -4 31.66666667z + z2 = 0 + -4 Combine like terms: 0 + -4 = -4 31.66666667z + z2 = -4 The z term is 31.66666667z. Take half its coefficient (15.83333334). Square it (250.6944447) and add it to both sides. Add '250.6944447' to each side of the equation. 31.66666667z + 250.6944447 + z2 = -4 + 250.6944447 Reorder the terms: 250.6944447 + 31.66666667z + z2 = -4 + 250.6944447 Combine like terms: -4 + 250.6944447 = 246.6944447 250.6944447 + 31.66666667z + z2 = 246.6944447 Factor a perfect square on the left side: (z + 15.83333334)(z + 15.83333334) = 246.6944447 Calculate the square root of the right side: 15.706509628 Break this problem into two subproblems by setting (z + 15.83333334) equal to 15.706509628 and -15.706509628.Subproblem 1
z + 15.83333334 = 15.706509628 Simplifying z + 15.83333334 = 15.706509628 Reorder the terms: 15.83333334 + z = 15.706509628 Solving 15.83333334 + z = 15.706509628 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-15.83333334' to each side of the equation. 15.83333334 + -15.83333334 + z = 15.706509628 + -15.83333334 Combine like terms: 15.83333334 + -15.83333334 = 0.00000000 0.00000000 + z = 15.706509628 + -15.83333334 z = 15.706509628 + -15.83333334 Combine like terms: 15.706509628 + -15.83333334 = -0.126823712 z = -0.126823712 Simplifying z = -0.126823712Subproblem 2
z + 15.83333334 = -15.706509628 Simplifying z + 15.83333334 = -15.706509628 Reorder the terms: 15.83333334 + z = -15.706509628 Solving 15.83333334 + z = -15.706509628 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-15.83333334' to each side of the equation. 15.83333334 + -15.83333334 + z = -15.706509628 + -15.83333334 Combine like terms: 15.83333334 + -15.83333334 = 0.00000000 0.00000000 + z = -15.706509628 + -15.83333334 z = -15.706509628 + -15.83333334 Combine like terms: -15.706509628 + -15.83333334 = -31.539842968 z = -31.539842968 Simplifying z = -31.539842968Solution
The solution to the problem is based on the solutions from the subproblems. z = {-0.126823712, -31.539842968}
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