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Simplifying 7q2 + 10q = 2q2 + 155 Reorder the terms: 10q + 7q2 = 2q2 + 155 Reorder the terms: 10q + 7q2 = 155 + 2q2 Solving 10q + 7q2 = 155 + 2q2 Solving for variable 'q'. Reorder the terms: -155 + 10q + 7q2 + -2q2 = 155 + 2q2 + -155 + -2q2 Combine like terms: 7q2 + -2q2 = 5q2 -155 + 10q + 5q2 = 155 + 2q2 + -155 + -2q2 Reorder the terms: -155 + 10q + 5q2 = 155 + -155 + 2q2 + -2q2 Combine like terms: 155 + -155 = 0 -155 + 10q + 5q2 = 0 + 2q2 + -2q2 -155 + 10q + 5q2 = 2q2 + -2q2 Combine like terms: 2q2 + -2q2 = 0 -155 + 10q + 5q2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-31 + 2q + q2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-31 + 2q + q2)' equal to zero and attempt to solve: Simplifying -31 + 2q + q2 = 0 Solving -31 + 2q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 2q + 31 + q2 = 0 + 31 Reorder the terms: -31 + 31 + 2q + q2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 2q + q2 = 0 + 31 2q + q2 = 0 + 31 Combine like terms: 0 + 31 = 31 2q + q2 = 31 The q term is 2q. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2q + 1 + q2 = 31 + 1 Reorder the terms: 1 + 2q + q2 = 31 + 1 Combine like terms: 31 + 1 = 32 1 + 2q + q2 = 32 Factor a perfect square on the left side: (q + 1)(q + 1) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (q + 1) equal to 5.656854249 and -5.656854249.Subproblem 1
q + 1 = 5.656854249 Simplifying q + 1 = 5.656854249 Reorder the terms: 1 + q = 5.656854249 Solving 1 + q = 5.656854249 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + q = 5.656854249 + -1 Combine like terms: 1 + -1 = 0 0 + q = 5.656854249 + -1 q = 5.656854249 + -1 Combine like terms: 5.656854249 + -1 = 4.656854249 q = 4.656854249 Simplifying q = 4.656854249Subproblem 2
q + 1 = -5.656854249 Simplifying q + 1 = -5.656854249 Reorder the terms: 1 + q = -5.656854249 Solving 1 + q = -5.656854249 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + q = -5.656854249 + -1 Combine like terms: 1 + -1 = 0 0 + q = -5.656854249 + -1 q = -5.656854249 + -1 Combine like terms: -5.656854249 + -1 = -6.656854249 q = -6.656854249 Simplifying q = -6.656854249Solution
The solution to the problem is based on the solutions from the subproblems. q = {4.656854249, -6.656854249}Solution
q = {4.656854249, -6.656854249}
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