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Simplifying q2 + 26q + 9 = 0 Reorder the terms: 9 + 26q + q2 = 0 Solving 9 + 26q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 26q + -9 + q2 = 0 + -9 Reorder the terms: 9 + -9 + 26q + q2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 26q + q2 = 0 + -9 26q + q2 = 0 + -9 Combine like terms: 0 + -9 = -9 26q + q2 = -9 The q term is 26q. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26q + 169 + q2 = -9 + 169 Reorder the terms: 169 + 26q + q2 = -9 + 169 Combine like terms: -9 + 169 = 160 169 + 26q + q2 = 160 Factor a perfect square on the left side: (q + 13)(q + 13) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (q + 13) equal to 12.649110641 and -12.649110641.Subproblem 1
q + 13 = 12.649110641 Simplifying q + 13 = 12.649110641 Reorder the terms: 13 + q = 12.649110641 Solving 13 + q = 12.649110641 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + q = 12.649110641 + -13 Combine like terms: 13 + -13 = 0 0 + q = 12.649110641 + -13 q = 12.649110641 + -13 Combine like terms: 12.649110641 + -13 = -0.350889359 q = -0.350889359 Simplifying q = -0.350889359Subproblem 2
q + 13 = -12.649110641 Simplifying q + 13 = -12.649110641 Reorder the terms: 13 + q = -12.649110641 Solving 13 + q = -12.649110641 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + q = -12.649110641 + -13 Combine like terms: 13 + -13 = 0 0 + q = -12.649110641 + -13 q = -12.649110641 + -13 Combine like terms: -12.649110641 + -13 = -25.649110641 q = -25.649110641 Simplifying q = -25.649110641Solution
The solution to the problem is based on the solutions from the subproblems. q = {-0.350889359, -25.649110641}
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