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Simplifying -114q + -120 + 26q2 = 0 Reorder the terms: -120 + -114q + 26q2 = 0 Solving -120 + -114q + 26q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '2'. 2(-60 + -57q + 13q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-60 + -57q + 13q2)' equal to zero and attempt to solve: Simplifying -60 + -57q + 13q2 = 0 Solving -60 + -57q + 13q2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -4.615384615 + -4.384615385q + q2 = 0 Move the constant term to the right: Add '4.615384615' to each side of the equation. -4.615384615 + -4.384615385q + 4.615384615 + q2 = 0 + 4.615384615 Reorder the terms: -4.615384615 + 4.615384615 + -4.384615385q + q2 = 0 + 4.615384615 Combine like terms: -4.615384615 + 4.615384615 = 0.000000000 0.000000000 + -4.384615385q + q2 = 0 + 4.615384615 -4.384615385q + q2 = 0 + 4.615384615 Combine like terms: 0 + 4.615384615 = 4.615384615 -4.384615385q + q2 = 4.615384615 The q term is -4.384615385q. Take half its coefficient (-2.192307693). Square it (4.806213021) and add it to both sides. Add '4.806213021' to each side of the equation. -4.384615385q + 4.806213021 + q2 = 4.615384615 + 4.806213021 Reorder the terms: 4.806213021 + -4.384615385q + q2 = 4.615384615 + 4.806213021 Combine like terms: 4.615384615 + 4.806213021 = 9.421597636 4.806213021 + -4.384615385q + q2 = 9.421597636 Factor a perfect square on the left side: (q + -2.192307693)(q + -2.192307693) = 9.421597636 Calculate the square root of the right side: 3.069462109 Break this problem into two subproblems by setting (q + -2.192307693) equal to 3.069462109 and -3.069462109.Subproblem 1
q + -2.192307693 = 3.069462109 Simplifying q + -2.192307693 = 3.069462109 Reorder the terms: -2.192307693 + q = 3.069462109 Solving -2.192307693 + q = 3.069462109 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2.192307693' to each side of the equation. -2.192307693 + 2.192307693 + q = 3.069462109 + 2.192307693 Combine like terms: -2.192307693 + 2.192307693 = 0.000000000 0.000000000 + q = 3.069462109 + 2.192307693 q = 3.069462109 + 2.192307693 Combine like terms: 3.069462109 + 2.192307693 = 5.261769802 q = 5.261769802 Simplifying q = 5.261769802Subproblem 2
q + -2.192307693 = -3.069462109 Simplifying q + -2.192307693 = -3.069462109 Reorder the terms: -2.192307693 + q = -3.069462109 Solving -2.192307693 + q = -3.069462109 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2.192307693' to each side of the equation. -2.192307693 + 2.192307693 + q = -3.069462109 + 2.192307693 Combine like terms: -2.192307693 + 2.192307693 = 0.000000000 0.000000000 + q = -3.069462109 + 2.192307693 q = -3.069462109 + 2.192307693 Combine like terms: -3.069462109 + 2.192307693 = -0.877154416 q = -0.877154416 Simplifying q = -0.877154416Solution
The solution to the problem is based on the solutions from the subproblems. q = {5.261769802, -0.877154416}Solution
q = {5.261769802, -0.877154416}
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