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Simplifying 15q + 3q2 + -12 = 0 Reorder the terms: -12 + 15q + 3q2 = 0 Solving -12 + 15q + 3q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 5q + q2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 5q + q2)' equal to zero and attempt to solve: Simplifying -4 + 5q + q2 = 0 Solving -4 + 5q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 5q + 4 + q2 = 0 + 4 Reorder the terms: -4 + 4 + 5q + q2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5q + q2 = 0 + 4 5q + q2 = 0 + 4 Combine like terms: 0 + 4 = 4 5q + q2 = 4 The q term is 5q. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5q + 6.25 + q2 = 4 + 6.25 Reorder the terms: 6.25 + 5q + q2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + 5q + q2 = 10.25 Factor a perfect square on the left side: (q + 2.5)(q + 2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (q + 2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
q + 2.5 = 3.201562119 Simplifying q + 2.5 = 3.201562119 Reorder the terms: 2.5 + q = 3.201562119 Solving 2.5 + q = 3.201562119 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + q = 3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + q = 3.201562119 + -2.5 q = 3.201562119 + -2.5 Combine like terms: 3.201562119 + -2.5 = 0.701562119 q = 0.701562119 Simplifying q = 0.701562119Subproblem 2
q + 2.5 = -3.201562119 Simplifying q + 2.5 = -3.201562119 Reorder the terms: 2.5 + q = -3.201562119 Solving 2.5 + q = -3.201562119 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + q = -3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + q = -3.201562119 + -2.5 q = -3.201562119 + -2.5 Combine like terms: -3.201562119 + -2.5 = -5.701562119 q = -5.701562119 Simplifying q = -5.701562119Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.701562119, -5.701562119}Solution
q = {0.701562119, -5.701562119}
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