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Simplifying q2 + -10q = 35 Reorder the terms: -10q + q2 = 35 Solving -10q + q2 = 35 Solving for variable 'q'. Reorder the terms: -35 + -10q + q2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -10q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -10q + 35 + q2 = 0 + 35 Reorder the terms: -35 + 35 + -10q + q2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -10q + q2 = 0 + 35 -10q + q2 = 0 + 35 Combine like terms: 0 + 35 = 35 -10q + q2 = 35 The q term is -10q. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10q + 25 + q2 = 35 + 25 Reorder the terms: 25 + -10q + q2 = 35 + 25 Combine like terms: 35 + 25 = 60 25 + -10q + q2 = 60 Factor a perfect square on the left side: (q + -5)(q + -5) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (q + -5) equal to 7.745966692 and -7.745966692.Subproblem 1
q + -5 = 7.745966692 Simplifying q + -5 = 7.745966692 Reorder the terms: -5 + q = 7.745966692 Solving -5 + q = 7.745966692 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + q = 7.745966692 + 5 Combine like terms: -5 + 5 = 0 0 + q = 7.745966692 + 5 q = 7.745966692 + 5 Combine like terms: 7.745966692 + 5 = 12.745966692 q = 12.745966692 Simplifying q = 12.745966692Subproblem 2
q + -5 = -7.745966692 Simplifying q + -5 = -7.745966692 Reorder the terms: -5 + q = -7.745966692 Solving -5 + q = -7.745966692 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + q = -7.745966692 + 5 Combine like terms: -5 + 5 = 0 0 + q = -7.745966692 + 5 q = -7.745966692 + 5 Combine like terms: -7.745966692 + 5 = -2.745966692 q = -2.745966692 Simplifying q = -2.745966692Solution
The solution to the problem is based on the solutions from the subproblems. q = {12.745966692, -2.745966692}
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