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Simplifying q2 + 60q + -675 = 0 Reorder the terms: -675 + 60q + q2 = 0 Solving -675 + 60q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '675' to each side of the equation. -675 + 60q + 675 + q2 = 0 + 675 Reorder the terms: -675 + 675 + 60q + q2 = 0 + 675 Combine like terms: -675 + 675 = 0 0 + 60q + q2 = 0 + 675 60q + q2 = 0 + 675 Combine like terms: 0 + 675 = 675 60q + q2 = 675 The q term is 60q. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60q + 900 + q2 = 675 + 900 Reorder the terms: 900 + 60q + q2 = 675 + 900 Combine like terms: 675 + 900 = 1575 900 + 60q + q2 = 1575 Factor a perfect square on the left side: (q + 30)(q + 30) = 1575 Calculate the square root of the right side: 39.686269666 Break this problem into two subproblems by setting (q + 30) equal to 39.686269666 and -39.686269666.Subproblem 1
q + 30 = 39.686269666 Simplifying q + 30 = 39.686269666 Reorder the terms: 30 + q = 39.686269666 Solving 30 + q = 39.686269666 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + q = 39.686269666 + -30 Combine like terms: 30 + -30 = 0 0 + q = 39.686269666 + -30 q = 39.686269666 + -30 Combine like terms: 39.686269666 + -30 = 9.686269666 q = 9.686269666 Simplifying q = 9.686269666Subproblem 2
q + 30 = -39.686269666 Simplifying q + 30 = -39.686269666 Reorder the terms: 30 + q = -39.686269666 Solving 30 + q = -39.686269666 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + q = -39.686269666 + -30 Combine like terms: 30 + -30 = 0 0 + q = -39.686269666 + -30 q = -39.686269666 + -30 Combine like terms: -39.686269666 + -30 = -69.686269666 q = -69.686269666 Simplifying q = -69.686269666Solution
The solution to the problem is based on the solutions from the subproblems. q = {9.686269666, -69.686269666}
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