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Simplifying 5q2 + 8q = 12 Reorder the terms: 8q + 5q2 = 12 Solving 8q + 5q2 = 12 Solving for variable 'q'. Reorder the terms: -12 + 8q + 5q2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 8q + 5q2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + 1.6q + q2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 1.6q + 2.4 + q2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 1.6q + q2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 1.6q + q2 = 0 + 2.4 1.6q + q2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 1.6q + q2 = 2.4 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 = 2.4 + 0.64 Reorder the terms: 0.64 + 1.6q + q2 = 2.4 + 0.64 Combine like terms: 2.4 + 0.64 = 3.04 0.64 + 1.6q + q2 = 3.04 Factor a perfect square on the left side: (q + 0.8)(q + 0.8) = 3.04 Calculate the square root of the right side: 1.743559577 Break this problem into two subproblems by setting (q + 0.8) equal to 1.743559577 and -1.743559577.Subproblem 1
q + 0.8 = 1.743559577 Simplifying q + 0.8 = 1.743559577 Reorder the terms: 0.8 + q = 1.743559577 Solving 0.8 + q = 1.743559577 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 = 1.743559577 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + q = 1.743559577 + -0.8 q = 1.743559577 + -0.8 Combine like terms: 1.743559577 + -0.8 = 0.943559577 q = 0.943559577 Simplifying q = 0.943559577Subproblem 2
q + 0.8 = -1.743559577 Simplifying q + 0.8 = -1.743559577 Reorder the terms: 0.8 + q = -1.743559577 Solving 0.8 + q = -1.743559577 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 = -1.743559577 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + q = -1.743559577 + -0.8 q = -1.743559577 + -0.8 Combine like terms: -1.743559577 + -0.8 = -2.543559577 q = -2.543559577 Simplifying q = -2.543559577Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.943559577, -2.543559577}
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