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Simplifying (3z2 + z + -4) + (2z2 + 2z + -3) = 0 Reorder the terms: (-4 + z + 3z2) + (2z2 + 2z + -3) = 0 Remove parenthesis around (-4 + z + 3z2) -4 + z + 3z2 + (2z2 + 2z + -3) = 0 Reorder the terms: -4 + z + 3z2 + (-3 + 2z + 2z2) = 0 Remove parenthesis around (-3 + 2z + 2z2) -4 + z + 3z2 + -3 + 2z + 2z2 = 0 Reorder the terms: -4 + -3 + z + 2z + 3z2 + 2z2 = 0 Combine like terms: -4 + -3 = -7 -7 + z + 2z + 3z2 + 2z2 = 0 Combine like terms: z + 2z = 3z -7 + 3z + 3z2 + 2z2 = 0 Combine like terms: 3z2 + 2z2 = 5z2 -7 + 3z + 5z2 = 0 Solving -7 + 3z + 5z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + 0.6z + z2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 0.6z + 1.4 + z2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 0.6z + z2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 0.6z + z2 = 0 + 1.4 0.6z + z2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 0.6z + z2 = 1.4 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 = 1.4 + 0.09 Reorder the terms: 0.09 + 0.6z + z2 = 1.4 + 0.09 Combine like terms: 1.4 + 0.09 = 1.49 0.09 + 0.6z + z2 = 1.49 Factor a perfect square on the left side: (z + 0.3)(z + 0.3) = 1.49 Calculate the square root of the right side: 1.220655562 Break this problem into two subproblems by setting (z + 0.3) equal to 1.220655562 and -1.220655562.Subproblem 1
z + 0.3 = 1.220655562 Simplifying z + 0.3 = 1.220655562 Reorder the terms: 0.3 + z = 1.220655562 Solving 0.3 + z = 1.220655562 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 = 1.220655562 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + z = 1.220655562 + -0.3 z = 1.220655562 + -0.3 Combine like terms: 1.220655562 + -0.3 = 0.920655562 z = 0.920655562 Simplifying z = 0.920655562Subproblem 2
z + 0.3 = -1.220655562 Simplifying z + 0.3 = -1.220655562 Reorder the terms: 0.3 + z = -1.220655562 Solving 0.3 + z = -1.220655562 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 = -1.220655562 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + z = -1.220655562 + -0.3 z = -1.220655562 + -0.3 Combine like terms: -1.220655562 + -0.3 = -1.520655562 z = -1.520655562 Simplifying z = -1.520655562Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.920655562, -1.520655562}
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