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Simplifying z2 + 10z = 25 Reorder the terms: 10z + z2 = 25 Solving 10z + z2 = 25 Solving for variable 'z'. Reorder the terms: -25 + 10z + z2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 10z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 10z + 25 + z2 = 0 + 25 Reorder the terms: -25 + 25 + 10z + z2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 10z + z2 = 0 + 25 10z + z2 = 0 + 25 Combine like terms: 0 + 25 = 25 10z + z2 = 25 The z term is 10z. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10z + 25 + z2 = 25 + 25 Reorder the terms: 25 + 10z + z2 = 25 + 25 Combine like terms: 25 + 25 = 50 25 + 10z + z2 = 50 Factor a perfect square on the left side: (z + 5)(z + 5) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (z + 5) equal to 7.071067812 and -7.071067812.Subproblem 1
z + 5 = 7.071067812 Simplifying z + 5 = 7.071067812 Reorder the terms: 5 + z = 7.071067812 Solving 5 + z = 7.071067812 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + z = 7.071067812 + -5 Combine like terms: 5 + -5 = 0 0 + z = 7.071067812 + -5 z = 7.071067812 + -5 Combine like terms: 7.071067812 + -5 = 2.071067812 z = 2.071067812 Simplifying z = 2.071067812Subproblem 2
z + 5 = -7.071067812 Simplifying z + 5 = -7.071067812 Reorder the terms: 5 + z = -7.071067812 Solving 5 + z = -7.071067812 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + z = -7.071067812 + -5 Combine like terms: 5 + -5 = 0 0 + z = -7.071067812 + -5 z = -7.071067812 + -5 Combine like terms: -7.071067812 + -5 = -12.071067812 z = -12.071067812 Simplifying z = -12.071067812Solution
The solution to the problem is based on the solutions from the subproblems. z = {2.071067812, -12.071067812}
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