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Simplifying q2 + -14q + 27 = 0 Reorder the terms: 27 + -14q + q2 = 0 Solving 27 + -14q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + -14q + -27 + q2 = 0 + -27 Reorder the terms: 27 + -27 + -14q + q2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -14q + q2 = 0 + -27 -14q + q2 = 0 + -27 Combine like terms: 0 + -27 = -27 -14q + q2 = -27 The q term is -14q. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14q + 49 + q2 = -27 + 49 Reorder the terms: 49 + -14q + q2 = -27 + 49 Combine like terms: -27 + 49 = 22 49 + -14q + q2 = 22 Factor a perfect square on the left side: (q + -7)(q + -7) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (q + -7) equal to 4.69041576 and -4.69041576.Subproblem 1
q + -7 = 4.69041576 Simplifying q + -7 = 4.69041576 Reorder the terms: -7 + q = 4.69041576 Solving -7 + q = 4.69041576 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + q = 4.69041576 + 7 Combine like terms: -7 + 7 = 0 0 + q = 4.69041576 + 7 q = 4.69041576 + 7 Combine like terms: 4.69041576 + 7 = 11.69041576 q = 11.69041576 Simplifying q = 11.69041576Subproblem 2
q + -7 = -4.69041576 Simplifying q + -7 = -4.69041576 Reorder the terms: -7 + q = -4.69041576 Solving -7 + q = -4.69041576 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + q = -4.69041576 + 7 Combine like terms: -7 + 7 = 0 0 + q = -4.69041576 + 7 q = -4.69041576 + 7 Combine like terms: -4.69041576 + 7 = 2.30958424 q = 2.30958424 Simplifying q = 2.30958424Solution
The solution to the problem is based on the solutions from the subproblems. q = {11.69041576, 2.30958424}
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