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Simplifying q4 + -15q2 + 36 = 0 Reorder the terms: 36 + -15q2 + q4 = 0 Solving 36 + -15q2 + q4 = 0 Solving for variable 'q'. Factor a trinomial. (3 + -1q2)(12 + -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 '(12 + -1q2)' equal to zero and attempt to solve: Simplifying 12 + -1q2 = 0 Solving 12 + -1q2 = 0 Move all terms containing q to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1q2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1q2 = 0 + -12 -1q2 = 0 + -12 Combine like terms: 0 + -12 = -12 -1q2 = -12 Divide each side by '-1'. q2 = 12 Simplifying q2 = 12 Take the square root of each side: q = {-3.464101615, 3.464101615}Solution
q = {-1.732050808, 1.732050808, -3.464101615, 3.464101615}
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