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Simplifying (-1z + 2.1)(3z + 3) = 0 Reorder the terms: (2.1 + -1z)(3z + 3) = 0 Reorder the terms: (2.1 + -1z)(3 + 3z) = 0 Multiply (2.1 + -1z) * (3 + 3z) (2.1(3 + 3z) + -1z * (3 + 3z)) = 0 ((3 * 2.1 + 3z * 2.1) + -1z * (3 + 3z)) = 0 ((6.3 + 6.3z) + -1z * (3 + 3z)) = 0 (6.3 + 6.3z + (3 * -1z + 3z * -1z)) = 0 (6.3 + 6.3z + (-3z + -3z2)) = 0 Combine like terms: 6.3z + -3z = 3.3z (6.3 + 3.3z + -3z2) = 0 Solving 6.3 + 3.3z + -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'. -2.1 + -1.1z + z2 = 0 Move the constant term to the right: Add '2.1' to each side of the equation. -2.1 + -1.1z + 2.1 + z2 = 0 + 2.1 Reorder the terms: -2.1 + 2.1 + -1.1z + z2 = 0 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + -1.1z + z2 = 0 + 2.1 -1.1z + z2 = 0 + 2.1 Combine like terms: 0 + 2.1 = 2.1 -1.1z + z2 = 2.1 The z term is -1.1z. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1z + 0.3025 + z2 = 2.1 + 0.3025 Reorder the terms: 0.3025 + -1.1z + z2 = 2.1 + 0.3025 Combine like terms: 2.1 + 0.3025 = 2.4025 0.3025 + -1.1z + z2 = 2.4025 Factor a perfect square on the left side: (z + -0.55)(z + -0.55) = 2.4025 Calculate the square root of the right side: 1.55 Break this problem into two subproblems by setting (z + -0.55) equal to 1.55 and -1.55.Subproblem 1
z + -0.55 = 1.55 Simplifying z + -0.55 = 1.55 Reorder the terms: -0.55 + z = 1.55 Solving -0.55 + z = 1.55 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + z = 1.55 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + z = 1.55 + 0.55 z = 1.55 + 0.55 Combine like terms: 1.55 + 0.55 = 2.1 z = 2.1 Simplifying z = 2.1Subproblem 2
z + -0.55 = -1.55 Simplifying z + -0.55 = -1.55 Reorder the terms: -0.55 + z = -1.55 Solving -0.55 + z = -1.55 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + z = -1.55 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + z = -1.55 + 0.55 z = -1.55 + 0.55 Combine like terms: -1.55 + 0.55 = -1 z = -1 Simplifying z = -1Solution
The solution to the problem is based on the solutions from the subproblems. z = {2.1, -1}
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