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Simplifying q4 + 15 = 8q2 Reorder the terms: 15 + q4 = 8q2 Solving 15 + q4 = 8q2 Solving for variable 'q'. Reorder the terms: 15 + -8q2 + q4 = 8q2 + -8q2 Combine like terms: 8q2 + -8q2 = 0 15 + -8q2 + q4 = 0 Factor a trinomial. (3 + -1q2)(5 + -1q2) = 0Subproblem 1
Set the factor '(3 + -1q2)' equal to zero and attempt to solve: Simplifying 3 + -1q2 = 0 Solving 3 + -1q2 = 0 Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1q2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1q2 = 0 + -3 -1q2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1q2 = -3 Divide each side by '-1'. q2 = 3 Simplifying q2 = 3 Take the square root of each side: q = {-1.732050808, 1.732050808}Subproblem 2
Set the factor '(5 + -1q2)' equal to zero and attempt to solve: Simplifying 5 + -1q2 = 0 Solving 5 + -1q2 = 0 Move all terms containing q to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1q2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1q2 = 0 + -5 -1q2 = 0 + -5 Combine like terms: 0 + -5 = -5 -1q2 = -5 Divide each side by '-1'. q2 = 5 Simplifying q2 = 5 Take the square root of each side: q = {-2.236067978, 2.236067978}Solution
q = {-1.732050808, 1.732050808, -2.236067978, 2.236067978}
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