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Simplifying 4.5 + 2z = 2z2 Solving 4.5 + 2z = 2z2 Solving for variable 'z'. Combine like terms: 2z2 + -2z2 = 0 4.5 + 2z + -2z2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.25 + -1z + z2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -1z + 2.25 + z2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -1z + z2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -1z + z2 = 0 + 2.25 -1z + z2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -1z + z2 = 2.25 The z term is -1z. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1z + 0.25 + z2 = 2.25 + 0.25 Reorder the terms: 0.25 + -1z + z2 = 2.25 + 0.25 Combine like terms: 2.25 + 0.25 = 2.5 0.25 + -1z + z2 = 2.5 Factor a perfect square on the left side: (z + -0.5)(z + -0.5) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (z + -0.5) equal to 1.58113883 and -1.58113883.Subproblem 1
z + -0.5 = 1.58113883 Simplifying z + -0.5 = 1.58113883 Reorder the terms: -0.5 + z = 1.58113883 Solving -0.5 + z = 1.58113883 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + z = 1.58113883 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = 1.58113883 + 0.5 z = 1.58113883 + 0.5 Combine like terms: 1.58113883 + 0.5 = 2.08113883 z = 2.08113883 Simplifying z = 2.08113883Subproblem 2
z + -0.5 = -1.58113883 Simplifying z + -0.5 = -1.58113883 Reorder the terms: -0.5 + z = -1.58113883 Solving -0.5 + z = -1.58113883 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + z = -1.58113883 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = -1.58113883 + 0.5 z = -1.58113883 + 0.5 Combine like terms: -1.58113883 + 0.5 = -1.08113883 z = -1.08113883 Simplifying z = -1.08113883Solution
The solution to the problem is based on the solutions from the subproblems. z = {2.08113883, -1.08113883}
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