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Simplifying q + q2 = 14 Solving q + q2 = 14 Solving for variable 'q'. Reorder the terms: -14 + q + q2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + q + 14 + q2 = 0 + 14 Reorder the terms: -14 + 14 + q + q2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + q + q2 = 0 + 14 q + q2 = 0 + 14 Combine like terms: 0 + 14 = 14 q + q2 = 14 The q term is q. 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. q + 0.25 + q2 = 14 + 0.25 Reorder the terms: 0.25 + q + q2 = 14 + 0.25 Combine like terms: 14 + 0.25 = 14.25 0.25 + q + q2 = 14.25 Factor a perfect square on the left side: (q + 0.5)(q + 0.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (q + 0.5) equal to 3.774917218 and -3.774917218.Subproblem 1
q + 0.5 = 3.774917218 Simplifying q + 0.5 = 3.774917218 Reorder the terms: 0.5 + q = 3.774917218 Solving 0.5 + q = 3.774917218 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + q = 3.774917218 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q = 3.774917218 + -0.5 q = 3.774917218 + -0.5 Combine like terms: 3.774917218 + -0.5 = 3.274917218 q = 3.274917218 Simplifying q = 3.274917218Subproblem 2
q + 0.5 = -3.774917218 Simplifying q + 0.5 = -3.774917218 Reorder the terms: 0.5 + q = -3.774917218 Solving 0.5 + q = -3.774917218 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + q = -3.774917218 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q = -3.774917218 + -0.5 q = -3.774917218 + -0.5 Combine like terms: -3.774917218 + -0.5 = -4.274917218 q = -4.274917218 Simplifying q = -4.274917218Solution
The solution to the problem is based on the solutions from the subproblems. q = {3.274917218, -4.274917218}
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