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Simplifying q2 + -24q + -43 = 0 Reorder the terms: -43 + -24q + q2 = 0 Solving -43 + -24q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -24q + 43 + q2 = 0 + 43 Reorder the terms: -43 + 43 + -24q + q2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -24q + q2 = 0 + 43 -24q + q2 = 0 + 43 Combine like terms: 0 + 43 = 43 -24q + q2 = 43 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 = 43 + 144 Reorder the terms: 144 + -24q + q2 = 43 + 144 Combine like terms: 43 + 144 = 187 144 + -24q + q2 = 187 Factor a perfect square on the left side: (q + -12)(q + -12) = 187 Calculate the square root of the right side: 13.674794331 Break this problem into two subproblems by setting (q + -12) equal to 13.674794331 and -13.674794331.Subproblem 1
q + -12 = 13.674794331 Simplifying q + -12 = 13.674794331 Reorder the terms: -12 + q = 13.674794331 Solving -12 + q = 13.674794331 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 = 13.674794331 + 12 Combine like terms: -12 + 12 = 0 0 + q = 13.674794331 + 12 q = 13.674794331 + 12 Combine like terms: 13.674794331 + 12 = 25.674794331 q = 25.674794331 Simplifying q = 25.674794331Subproblem 2
q + -12 = -13.674794331 Simplifying q + -12 = -13.674794331 Reorder the terms: -12 + q = -13.674794331 Solving -12 + q = -13.674794331 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 = -13.674794331 + 12 Combine like terms: -12 + 12 = 0 0 + q = -13.674794331 + 12 q = -13.674794331 + 12 Combine like terms: -13.674794331 + 12 = -1.674794331 q = -1.674794331 Simplifying q = -1.674794331Solution
The solution to the problem is based on the solutions from the subproblems. q = {25.674794331, -1.674794331}
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