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Simplifying q2 + -12q + 26 = 0 Reorder the terms: 26 + -12q + q2 = 0 Solving 26 + -12q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + -12q + -26 + q2 = 0 + -26 Reorder the terms: 26 + -26 + -12q + q2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -12q + q2 = 0 + -26 -12q + q2 = 0 + -26 Combine like terms: 0 + -26 = -26 -12q + q2 = -26 The q term is -12q. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12q + 36 + q2 = -26 + 36 Reorder the terms: 36 + -12q + q2 = -26 + 36 Combine like terms: -26 + 36 = 10 36 + -12q + q2 = 10 Factor a perfect square on the left side: (q + -6)(q + -6) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (q + -6) equal to 3.16227766 and -3.16227766.Subproblem 1
q + -6 = 3.16227766 Simplifying q + -6 = 3.16227766 Reorder the terms: -6 + q = 3.16227766 Solving -6 + q = 3.16227766 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + q = 3.16227766 + 6 Combine like terms: -6 + 6 = 0 0 + q = 3.16227766 + 6 q = 3.16227766 + 6 Combine like terms: 3.16227766 + 6 = 9.16227766 q = 9.16227766 Simplifying q = 9.16227766Subproblem 2
q + -6 = -3.16227766 Simplifying q + -6 = -3.16227766 Reorder the terms: -6 + q = -3.16227766 Solving -6 + q = -3.16227766 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + q = -3.16227766 + 6 Combine like terms: -6 + 6 = 0 0 + q = -3.16227766 + 6 q = -3.16227766 + 6 Combine like terms: -3.16227766 + 6 = 2.83772234 q = 2.83772234 Simplifying q = 2.83772234Solution
The solution to the problem is based on the solutions from the subproblems. q = {9.16227766, 2.83772234}
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