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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 = 147 144 + -24q + q2 = 147 Factor a perfect square on the left side: (q + -12)(q + -12) = 147 Calculate the square root of the right side: 12.124355653 Break this problem into two subproblems by setting (q + -12) equal to 12.124355653 and -12.124355653.Subproblem 1
q + -12 = 12.124355653 Simplifying q + -12 = 12.124355653 Reorder the terms: -12 + q = 12.124355653 Solving -12 + q = 12.124355653 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 = 12.124355653 + 12 Combine like terms: -12 + 12 = 0 0 + q = 12.124355653 + 12 q = 12.124355653 + 12 Combine like terms: 12.124355653 + 12 = 24.124355653 q = 24.124355653 Simplifying q = 24.124355653Subproblem 2
q + -12 = -12.124355653 Simplifying q + -12 = -12.124355653 Reorder the terms: -12 + q = -12.124355653 Solving -12 + q = -12.124355653 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 = -12.124355653 + 12 Combine like terms: -12 + 12 = 0 0 + q = -12.124355653 + 12 q = -12.124355653 + 12 Combine like terms: -12.124355653 + 12 = -0.124355653 q = -0.124355653 Simplifying q = -0.124355653Solution
The solution to the problem is based on the solutions from the subproblems. q = {24.124355653, -0.124355653}
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