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Simplifying q2 + -13q + 10 = 0 Reorder the terms: 10 + -13q + q2 = 0 Solving 10 + -13q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -13q + -10 + q2 = 0 + -10 Reorder the terms: 10 + -10 + -13q + q2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -13q + q2 = 0 + -10 -13q + q2 = 0 + -10 Combine like terms: 0 + -10 = -10 -13q + q2 = -10 The q term is -13q. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13q + 42.25 + q2 = -10 + 42.25 Reorder the terms: 42.25 + -13q + q2 = -10 + 42.25 Combine like terms: -10 + 42.25 = 32.25 42.25 + -13q + q2 = 32.25 Factor a perfect square on the left side: (q + -6.5)(q + -6.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (q + -6.5) equal to 5.678908346 and -5.678908346.Subproblem 1
q + -6.5 = 5.678908346 Simplifying q + -6.5 = 5.678908346 Reorder the terms: -6.5 + q = 5.678908346 Solving -6.5 + q = 5.678908346 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + q = 5.678908346 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + q = 5.678908346 + 6.5 q = 5.678908346 + 6.5 Combine like terms: 5.678908346 + 6.5 = 12.178908346 q = 12.178908346 Simplifying q = 12.178908346Subproblem 2
q + -6.5 = -5.678908346 Simplifying q + -6.5 = -5.678908346 Reorder the terms: -6.5 + q = -5.678908346 Solving -6.5 + q = -5.678908346 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + q = -5.678908346 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + q = -5.678908346 + 6.5 q = -5.678908346 + 6.5 Combine like terms: -5.678908346 + 6.5 = 0.821091654 q = 0.821091654 Simplifying q = 0.821091654Solution
The solution to the problem is based on the solutions from the subproblems. q = {12.178908346, 0.821091654}
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