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Simplifying z2 + -1z = 25 Reorder the terms: -1z + z2 = 25 Solving -1z + z2 = 25 Solving for variable 'z'. Reorder the terms: -25 + -1z + z2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -1z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -1z + 25 + z2 = 0 + 25 Reorder the terms: -25 + 25 + -1z + z2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -1z + z2 = 0 + 25 -1z + z2 = 0 + 25 Combine like terms: 0 + 25 = 25 -1z + z2 = 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 = 25 + 0.25 Reorder the terms: 0.25 + -1z + z2 = 25 + 0.25 Combine like terms: 25 + 0.25 = 25.25 0.25 + -1z + z2 = 25.25 Factor a perfect square on the left side: (z + -0.5)(z + -0.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (z + -0.5) equal to 5.024937811 and -5.024937811.Subproblem 1
z + -0.5 = 5.024937811 Simplifying z + -0.5 = 5.024937811 Reorder the terms: -0.5 + z = 5.024937811 Solving -0.5 + z = 5.024937811 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 = 5.024937811 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = 5.024937811 + 0.5 z = 5.024937811 + 0.5 Combine like terms: 5.024937811 + 0.5 = 5.524937811 z = 5.524937811 Simplifying z = 5.524937811Subproblem 2
z + -0.5 = -5.024937811 Simplifying z + -0.5 = -5.024937811 Reorder the terms: -0.5 + z = -5.024937811 Solving -0.5 + z = -5.024937811 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 = -5.024937811 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = -5.024937811 + 0.5 z = -5.024937811 + 0.5 Combine like terms: -5.024937811 + 0.5 = -4.524937811 z = -4.524937811 Simplifying z = -4.524937811Solution
The solution to the problem is based on the solutions from the subproblems. z = {5.524937811, -4.524937811}
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