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Simplifying q2 + -14q + 36 = 0 Reorder the terms: 36 + -14q + q2 = 0 Solving 36 + -14q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -14q + -36 + q2 = 0 + -36 Reorder the terms: 36 + -36 + -14q + q2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -14q + q2 = 0 + -36 -14q + q2 = 0 + -36 Combine like terms: 0 + -36 = -36 -14q + q2 = -36 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 = -36 + 49 Reorder the terms: 49 + -14q + q2 = -36 + 49 Combine like terms: -36 + 49 = 13 49 + -14q + q2 = 13 Factor a perfect square on the left side: (q + -7)(q + -7) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (q + -7) equal to 3.605551275 and -3.605551275.Subproblem 1
q + -7 = 3.605551275 Simplifying q + -7 = 3.605551275 Reorder the terms: -7 + q = 3.605551275 Solving -7 + q = 3.605551275 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 = 3.605551275 + 7 Combine like terms: -7 + 7 = 0 0 + q = 3.605551275 + 7 q = 3.605551275 + 7 Combine like terms: 3.605551275 + 7 = 10.605551275 q = 10.605551275 Simplifying q = 10.605551275Subproblem 2
q + -7 = -3.605551275 Simplifying q + -7 = -3.605551275 Reorder the terms: -7 + q = -3.605551275 Solving -7 + q = -3.605551275 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 = -3.605551275 + 7 Combine like terms: -7 + 7 = 0 0 + q = -3.605551275 + 7 q = -3.605551275 + 7 Combine like terms: -3.605551275 + 7 = 3.394448725 q = 3.394448725 Simplifying q = 3.394448725Solution
The solution to the problem is based on the solutions from the subproblems. q = {10.605551275, 3.394448725}
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