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Simplifying q2 + -14q = 45 Reorder the terms: -14q + q2 = 45 Solving -14q + q2 = 45 Solving for variable 'q'. Reorder the terms: -45 + -14q + q2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -14q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -14q + 45 + q2 = 0 + 45 Reorder the terms: -45 + 45 + -14q + q2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -14q + q2 = 0 + 45 -14q + q2 = 0 + 45 Combine like terms: 0 + 45 = 45 -14q + q2 = 45 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 = 45 + 49 Reorder the terms: 49 + -14q + q2 = 45 + 49 Combine like terms: 45 + 49 = 94 49 + -14q + q2 = 94 Factor a perfect square on the left side: (q + -7)(q + -7) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (q + -7) equal to 9.695359715 and -9.695359715.Subproblem 1
q + -7 = 9.695359715 Simplifying q + -7 = 9.695359715 Reorder the terms: -7 + q = 9.695359715 Solving -7 + q = 9.695359715 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 = 9.695359715 + 7 Combine like terms: -7 + 7 = 0 0 + q = 9.695359715 + 7 q = 9.695359715 + 7 Combine like terms: 9.695359715 + 7 = 16.695359715 q = 16.695359715 Simplifying q = 16.695359715Subproblem 2
q + -7 = -9.695359715 Simplifying q + -7 = -9.695359715 Reorder the terms: -7 + q = -9.695359715 Solving -7 + q = -9.695359715 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 = -9.695359715 + 7 Combine like terms: -7 + 7 = 0 0 + q = -9.695359715 + 7 q = -9.695359715 + 7 Combine like terms: -9.695359715 + 7 = -2.695359715 q = -2.695359715 Simplifying q = -2.695359715Solution
The solution to the problem is based on the solutions from the subproblems. q = {16.695359715, -2.695359715}
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