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Simplifying q2 + 16q + -25 = 0 Reorder the terms: -25 + 16q + q2 = 0 Solving -25 + 16q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 16q + 25 + q2 = 0 + 25 Reorder the terms: -25 + 25 + 16q + q2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 16q + q2 = 0 + 25 16q + q2 = 0 + 25 Combine like terms: 0 + 25 = 25 16q + q2 = 25 The q term is 16q. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16q + 64 + q2 = 25 + 64 Reorder the terms: 64 + 16q + q2 = 25 + 64 Combine like terms: 25 + 64 = 89 64 + 16q + q2 = 89 Factor a perfect square on the left side: (q + 8)(q + 8) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (q + 8) equal to 9.433981132 and -9.433981132.Subproblem 1
q + 8 = 9.433981132 Simplifying q + 8 = 9.433981132 Reorder the terms: 8 + q = 9.433981132 Solving 8 + q = 9.433981132 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + q = 9.433981132 + -8 Combine like terms: 8 + -8 = 0 0 + q = 9.433981132 + -8 q = 9.433981132 + -8 Combine like terms: 9.433981132 + -8 = 1.433981132 q = 1.433981132 Simplifying q = 1.433981132Subproblem 2
q + 8 = -9.433981132 Simplifying q + 8 = -9.433981132 Reorder the terms: 8 + q = -9.433981132 Solving 8 + q = -9.433981132 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + q = -9.433981132 + -8 Combine like terms: 8 + -8 = 0 0 + q = -9.433981132 + -8 q = -9.433981132 + -8 Combine like terms: -9.433981132 + -8 = -17.433981132 q = -17.433981132 Simplifying q = -17.433981132Solution
The solution to the problem is based on the solutions from the subproblems. q = {1.433981132, -17.433981132}
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