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Simplifying q2 + (4q2)(q2) = 1000 Remove parenthesis around (4q2) q2 + 4q2(q2) = 1000 Multiply q2 * q2 q2 + 4q4 = 1000 Solving q2 + 4q4 = 1000 Solving for variable 'q'. Reorder the terms: -1000 + q2 + 4q4 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -1000 + q2 + 4q4 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -250 + 0.25q2 + q4 = 0 Move the constant term to the right: Add '250' to each side of the equation. -250 + 0.25q2 + 250 + q4 = 0 + 250 Reorder the terms: -250 + 250 + 0.25q2 + q4 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 0.25q2 + q4 = 0 + 250 0.25q2 + q4 = 0 + 250 Combine like terms: 0 + 250 = 250 0.25q2 + q4 = 250 The q term is q2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25q2 + 0.25 + q4 = 250 + 0.25 Reorder the terms: 0.25 + 0.25q2 + q4 = 250 + 0.25 Combine like terms: 250 + 0.25 = 250.25 0.25 + 0.25q2 + q4 = 250.25 Factor a perfect square on the left side: (q2 + 0.5)(q2 + 0.5) = 250.25 Calculate the square root of the right side: 15.81929202 Break this problem into two subproblems by setting (q2 + 0.5) equal to 15.81929202 and -15.81929202.Subproblem 1
q2 + 0.5 = 15.81929202 Simplifying q2 + 0.5 = 15.81929202 Reorder the terms: 0.5 + q2 = 15.81929202 Solving 0.5 + q2 = 15.81929202 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + q2 = 15.81929202 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q2 = 15.81929202 + -0.5 q2 = 15.81929202 + -0.5 Combine like terms: 15.81929202 + -0.5 = 15.31929202 q2 = 15.31929202 Simplifying q2 = 15.31929202 Take the square root of each side: q = {-3.913986717, 3.913986717}Subproblem 2
q2 + 0.5 = -15.81929202 Simplifying q2 + 0.5 = -15.81929202 Reorder the terms: 0.5 + q2 = -15.81929202 Solving 0.5 + q2 = -15.81929202 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + q2 = -15.81929202 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q2 = -15.81929202 + -0.5 q2 = -15.81929202 + -0.5 Combine like terms: -15.81929202 + -0.5 = -16.31929202 q2 = -16.31929202 Simplifying q2 = -16.31929202 Reorder the terms: 16.31929202 + q2 = -16.31929202 + 16.31929202 Combine like terms: -16.31929202 + 16.31929202 = 0.00000000 16.31929202 + q2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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