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Simplifying 5q2 + 8q = 80 Reorder the terms: 8q + 5q2 = 80 Solving 8q + 5q2 = 80 Solving for variable 'q'. Reorder the terms: -80 + 8q + 5q2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + 8q + 5q2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -16 + 1.6q + q2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 1.6q + 16 + q2 = 0 + 16 Reorder the terms: -16 + 16 + 1.6q + q2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 1.6q + q2 = 0 + 16 1.6q + q2 = 0 + 16 Combine like terms: 0 + 16 = 16 1.6q + q2 = 16 The q term is 1.6q. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6q + 0.64 + q2 = 16 + 0.64 Reorder the terms: 0.64 + 1.6q + q2 = 16 + 0.64 Combine like terms: 16 + 0.64 = 16.64 0.64 + 1.6q + q2 = 16.64 Factor a perfect square on the left side: (q + 0.8)(q + 0.8) = 16.64 Calculate the square root of the right side: 4.079215611 Break this problem into two subproblems by setting (q + 0.8) equal to 4.079215611 and -4.079215611.Subproblem 1
q + 0.8 = 4.079215611 Simplifying q + 0.8 = 4.079215611 Reorder the terms: 0.8 + q = 4.079215611 Solving 0.8 + q = 4.079215611 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + q = 4.079215611 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + q = 4.079215611 + -0.8 q = 4.079215611 + -0.8 Combine like terms: 4.079215611 + -0.8 = 3.279215611 q = 3.279215611 Simplifying q = 3.279215611Subproblem 2
q + 0.8 = -4.079215611 Simplifying q + 0.8 = -4.079215611 Reorder the terms: 0.8 + q = -4.079215611 Solving 0.8 + q = -4.079215611 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + q = -4.079215611 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + q = -4.079215611 + -0.8 q = -4.079215611 + -0.8 Combine like terms: -4.079215611 + -0.8 = -4.879215611 q = -4.879215611 Simplifying q = -4.879215611Solution
The solution to the problem is based on the solutions from the subproblems. q = {3.279215611, -4.879215611}
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