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Simplifying q2 + -24q + 3 = 0 Reorder the terms: 3 + -24q + q2 = 0 Solving 3 + -24q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -24q + -3 + q2 = 0 + -3 Reorder the terms: 3 + -3 + -24q + q2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -24q + q2 = 0 + -3 -24q + q2 = 0 + -3 Combine like terms: 0 + -3 = -3 -24q + q2 = -3 The q term is -24q. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24q + 144 + q2 = -3 + 144 Reorder the terms: 144 + -24q + q2 = -3 + 144 Combine like terms: -3 + 144 = 141 144 + -24q + q2 = 141 Factor a perfect square on the left side: (q + -12)(q + -12) = 141 Calculate the square root of the right side: 11.874342087 Break this problem into two subproblems by setting (q + -12) equal to 11.874342087 and -11.874342087.Subproblem 1
q + -12 = 11.874342087 Simplifying q + -12 = 11.874342087 Reorder the terms: -12 + q = 11.874342087 Solving -12 + q = 11.874342087 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + q = 11.874342087 + 12 Combine like terms: -12 + 12 = 0 0 + q = 11.874342087 + 12 q = 11.874342087 + 12 Combine like terms: 11.874342087 + 12 = 23.874342087 q = 23.874342087 Simplifying q = 23.874342087Subproblem 2
q + -12 = -11.874342087 Simplifying q + -12 = -11.874342087 Reorder the terms: -12 + q = -11.874342087 Solving -12 + q = -11.874342087 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + q = -11.874342087 + 12 Combine like terms: -12 + 12 = 0 0 + q = -11.874342087 + 12 q = -11.874342087 + 12 Combine like terms: -11.874342087 + 12 = 0.125657913 q = 0.125657913 Simplifying q = 0.125657913Solution
The solution to the problem is based on the solutions from the subproblems. q = {23.874342087, 0.125657913}
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