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Simplifying 5 + -2z + -1z2 = 0 Solving 5 + -2z + -1z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 2z + z2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 2z + 5 + z2 = 0 + 5 Reorder the terms: -5 + 5 + 2z + z2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2z + z2 = 0 + 5 2z + z2 = 0 + 5 Combine like terms: 0 + 5 = 5 2z + z2 = 5 The z term is 2z. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2z + 1 + z2 = 5 + 1 Reorder the terms: 1 + 2z + z2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + 2z + z2 = 6 Factor a perfect square on the left side: (z + 1)(z + 1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (z + 1) equal to 2.449489743 and -2.449489743.Subproblem 1
z + 1 = 2.449489743 Simplifying z + 1 = 2.449489743 Reorder the terms: 1 + z = 2.449489743 Solving 1 + z = 2.449489743 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + z = 2.449489743 + -1 z = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 z = 1.449489743 Simplifying z = 1.449489743Subproblem 2
z + 1 = -2.449489743 Simplifying z + 1 = -2.449489743 Reorder the terms: 1 + z = -2.449489743 Solving 1 + z = -2.449489743 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + z = -2.449489743 + -1 z = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 z = -3.449489743 Simplifying z = -3.449489743Solution
The solution to the problem is based on the solutions from the subproblems. z = {1.449489743, -3.449489743}
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