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Simplifying 2q2 + -8q = 40 Reorder the terms: -8q + 2q2 = 40 Solving -8q + 2q2 = 40 Solving for variable 'q'. Reorder the terms: -40 + -8q + 2q2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + -8q + 2q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + -4q + q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20 + -4q + q2)' equal to zero and attempt to solve: Simplifying -20 + -4q + q2 = 0 Solving -20 + -4q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -4q + 20 + q2 = 0 + 20 Reorder the terms: -20 + 20 + -4q + q2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -4q + q2 = 0 + 20 -4q + q2 = 0 + 20 Combine like terms: 0 + 20 = 20 -4q + q2 = 20 The q term is -4q. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4q + 4 + q2 = 20 + 4 Reorder the terms: 4 + -4q + q2 = 20 + 4 Combine like terms: 20 + 4 = 24 4 + -4q + q2 = 24 Factor a perfect square on the left side: (q + -2)(q + -2) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (q + -2) equal to 4.898979486 and -4.898979486.Subproblem 1
q + -2 = 4.898979486 Simplifying q + -2 = 4.898979486 Reorder the terms: -2 + q = 4.898979486 Solving -2 + q = 4.898979486 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + q = 4.898979486 + 2 Combine like terms: -2 + 2 = 0 0 + q = 4.898979486 + 2 q = 4.898979486 + 2 Combine like terms: 4.898979486 + 2 = 6.898979486 q = 6.898979486 Simplifying q = 6.898979486Subproblem 2
q + -2 = -4.898979486 Simplifying q + -2 = -4.898979486 Reorder the terms: -2 + q = -4.898979486 Solving -2 + q = -4.898979486 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + q = -4.898979486 + 2 Combine like terms: -2 + 2 = 0 0 + q = -4.898979486 + 2 q = -4.898979486 + 2 Combine like terms: -4.898979486 + 2 = -2.898979486 q = -2.898979486 Simplifying q = -2.898979486Solution
The solution to the problem is based on the solutions from the subproblems. q = {6.898979486, -2.898979486}Solution
q = {6.898979486, -2.898979486}
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