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Simplifying 2q2 + 14q + -5 = 0 Reorder the terms: -5 + 14q + 2q2 = 0 Solving -5 + 14q + 2q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 7q + q2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 7q + 2.5 + q2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 7q + q2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 7q + q2 = 0 + 2.5 7q + q2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 7q + q2 = 2.5 The q term is 7q. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7q + 12.25 + q2 = 2.5 + 12.25 Reorder the terms: 12.25 + 7q + q2 = 2.5 + 12.25 Combine like terms: 2.5 + 12.25 = 14.75 12.25 + 7q + q2 = 14.75 Factor a perfect square on the left side: (q + 3.5)(q + 3.5) = 14.75 Calculate the square root of the right side: 3.840572874 Break this problem into two subproblems by setting (q + 3.5) equal to 3.840572874 and -3.840572874.Subproblem 1
q + 3.5 = 3.840572874 Simplifying q + 3.5 = 3.840572874 Reorder the terms: 3.5 + q = 3.840572874 Solving 3.5 + q = 3.840572874 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + q = 3.840572874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + q = 3.840572874 + -3.5 q = 3.840572874 + -3.5 Combine like terms: 3.840572874 + -3.5 = 0.340572874 q = 0.340572874 Simplifying q = 0.340572874Subproblem 2
q + 3.5 = -3.840572874 Simplifying q + 3.5 = -3.840572874 Reorder the terms: 3.5 + q = -3.840572874 Solving 3.5 + q = -3.840572874 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + q = -3.840572874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + q = -3.840572874 + -3.5 q = -3.840572874 + -3.5 Combine like terms: -3.840572874 + -3.5 = -7.340572874 q = -7.340572874 Simplifying q = -7.340572874Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.340572874, -7.340572874}
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