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Simplifying -2q2 + -4q = -8 Reorder the terms: -4q + -2q2 = -8 Solving -4q + -2q2 = -8 Solving for variable 'q'. Reorder the terms: 8 + -4q + -2q2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + -4q + -2q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -2q + -1q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -2q + -1q2)' equal to zero and attempt to solve: Simplifying 4 + -2q + -1q2 = 0 Solving 4 + -2q + -1q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + 2q + q2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 2q + 4 + q2 = 0 + 4 Reorder the terms: -4 + 4 + 2q + q2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2q + q2 = 0 + 4 2q + q2 = 0 + 4 Combine like terms: 0 + 4 = 4 2q + q2 = 4 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 = 4 + 1 Reorder the terms: 1 + 2q + q2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + 2q + q2 = 5 Factor a perfect square on the left side: (q + 1)(q + 1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (q + 1) equal to 2.236067978 and -2.236067978.Subproblem 1
q + 1 = 2.236067978 Simplifying q + 1 = 2.236067978 Reorder the terms: 1 + q = 2.236067978 Solving 1 + q = 2.236067978 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 = 2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + q = 2.236067978 + -1 q = 2.236067978 + -1 Combine like terms: 2.236067978 + -1 = 1.236067978 q = 1.236067978 Simplifying q = 1.236067978Subproblem 2
q + 1 = -2.236067978 Simplifying q + 1 = -2.236067978 Reorder the terms: 1 + q = -2.236067978 Solving 1 + q = -2.236067978 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 = -2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + q = -2.236067978 + -1 q = -2.236067978 + -1 Combine like terms: -2.236067978 + -1 = -3.236067978 q = -3.236067978 Simplifying q = -3.236067978Solution
The solution to the problem is based on the solutions from the subproblems. q = {1.236067978, -3.236067978}Solution
q = {1.236067978, -3.236067978}
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