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Simplifying q2 + -15q + 35 = 0 Reorder the terms: 35 + -15q + q2 = 0 Solving 35 + -15q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + -15q + -35 + q2 = 0 + -35 Reorder the terms: 35 + -35 + -15q + q2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -15q + q2 = 0 + -35 -15q + q2 = 0 + -35 Combine like terms: 0 + -35 = -35 -15q + q2 = -35 The q term is -15q. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15q + 56.25 + q2 = -35 + 56.25 Reorder the terms: 56.25 + -15q + q2 = -35 + 56.25 Combine like terms: -35 + 56.25 = 21.25 56.25 + -15q + q2 = 21.25 Factor a perfect square on the left side: (q + -7.5)(q + -7.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (q + -7.5) equal to 4.609772229 and -4.609772229.Subproblem 1
q + -7.5 = 4.609772229 Simplifying q + -7.5 = 4.609772229 Reorder the terms: -7.5 + q = 4.609772229 Solving -7.5 + q = 4.609772229 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + q = 4.609772229 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + q = 4.609772229 + 7.5 q = 4.609772229 + 7.5 Combine like terms: 4.609772229 + 7.5 = 12.109772229 q = 12.109772229 Simplifying q = 12.109772229Subproblem 2
q + -7.5 = -4.609772229 Simplifying q + -7.5 = -4.609772229 Reorder the terms: -7.5 + q = -4.609772229 Solving -7.5 + q = -4.609772229 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + q = -4.609772229 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + q = -4.609772229 + 7.5 q = -4.609772229 + 7.5 Combine like terms: -4.609772229 + 7.5 = 2.890227771 q = 2.890227771 Simplifying q = 2.890227771Solution
The solution to the problem is based on the solutions from the subproblems. q = {12.109772229, 2.890227771}
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