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Simplifying -4q2 + -8q + 36 = 0 Reorder the terms: 36 + -8q + -4q2 = 0 Solving 36 + -8q + -4q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '4'. 4(9 + -2q + -1q2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(9 + -2q + -1q2)' equal to zero and attempt to solve: Simplifying 9 + -2q + -1q2 = 0 Solving 9 + -2q + -1q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + 2q + q2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 2q + 9 + q2 = 0 + 9 Reorder the terms: -9 + 9 + 2q + q2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2q + q2 = 0 + 9 2q + q2 = 0 + 9 Combine like terms: 0 + 9 = 9 2q + q2 = 9 The q term is 2q. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2q + 1 + q2 = 9 + 1 Reorder the terms: 1 + 2q + q2 = 9 + 1 Combine like terms: 9 + 1 = 10 1 + 2q + q2 = 10 Factor a perfect square on the left side: (q + 1)(q + 1) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (q + 1) equal to 3.16227766 and -3.16227766.Subproblem 1
q + 1 = 3.16227766 Simplifying q + 1 = 3.16227766 Reorder the terms: 1 + q = 3.16227766 Solving 1 + q = 3.16227766 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + q = 3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + q = 3.16227766 + -1 q = 3.16227766 + -1 Combine like terms: 3.16227766 + -1 = 2.16227766 q = 2.16227766 Simplifying q = 2.16227766Subproblem 2
q + 1 = -3.16227766 Simplifying q + 1 = -3.16227766 Reorder the terms: 1 + q = -3.16227766 Solving 1 + q = -3.16227766 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + q = -3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + q = -3.16227766 + -1 q = -3.16227766 + -1 Combine like terms: -3.16227766 + -1 = -4.16227766 q = -4.16227766 Simplifying q = -4.16227766Solution
The solution to the problem is based on the solutions from the subproblems. q = {2.16227766, -4.16227766}Solution
q = {2.16227766, -4.16227766}
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