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Simplifying 11q2 + -999800q + 10000 = 0 Reorder the terms: 10000 + -999800q + 11q2 = 0 Solving 10000 + -999800q + 11q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 909.0909091 + -90890.90909q + q2 = 0 Move the constant term to the right: Add '-909.0909091' to each side of the equation. 909.0909091 + -90890.90909q + -909.0909091 + q2 = 0 + -909.0909091 Reorder the terms: 909.0909091 + -909.0909091 + -90890.90909q + q2 = 0 + -909.0909091 Combine like terms: 909.0909091 + -909.0909091 = 0.0000000 0.0000000 + -90890.90909q + q2 = 0 + -909.0909091 -90890.90909q + q2 = 0 + -909.0909091 Combine like terms: 0 + -909.0909091 = -909.0909091 -90890.90909q + q2 = -909.0909091 The q term is -90890.90909q. Take half its coefficient (-45445.45455). Square it (2065289339) and add it to both sides. Add '2065289339' to each side of the equation. -90890.90909q + 2065289339 + q2 = -909.0909091 + 2065289339 Reorder the terms: 2065289339 + -90890.90909q + q2 = -909.0909091 + 2065289339 Combine like terms: -909.0909091 + 2065289339 = 2065288429.9090909 2065289339 + -90890.90909q + q2 = 2065288429.9090909 Factor a perfect square on the left side: (q + -45445.45455)(q + -45445.45455) = 2065288429.9090909 Calculate the square root of the right side: 45445.444545181 Break this problem into two subproblems by setting (q + -45445.45455) equal to 45445.444545181 and -45445.444545181.Subproblem 1
q + -45445.45455 = 45445.444545181 Simplifying q + -45445.45455 = 45445.444545181 Reorder the terms: -45445.45455 + q = 45445.444545181 Solving -45445.45455 + q = 45445.444545181 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '45445.45455' to each side of the equation. -45445.45455 + 45445.45455 + q = 45445.444545181 + 45445.45455 Combine like terms: -45445.45455 + 45445.45455 = 0.00000 0.00000 + q = 45445.444545181 + 45445.45455 q = 45445.444545181 + 45445.45455 Combine like terms: 45445.444545181 + 45445.45455 = 90890.899095181 q = 90890.899095181 Simplifying q = 90890.899095181Subproblem 2
q + -45445.45455 = -45445.444545181 Simplifying q + -45445.45455 = -45445.444545181 Reorder the terms: -45445.45455 + q = -45445.444545181 Solving -45445.45455 + q = -45445.444545181 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '45445.45455' to each side of the equation. -45445.45455 + 45445.45455 + q = -45445.444545181 + 45445.45455 Combine like terms: -45445.45455 + 45445.45455 = 0.00000 0.00000 + q = -45445.444545181 + 45445.45455 q = -45445.444545181 + 45445.45455 Combine like terms: -45445.444545181 + 45445.45455 = 0.010004819 q = 0.010004819 Simplifying q = 0.010004819Solution
The solution to the problem is based on the solutions from the subproblems. q = {90890.899095181, 0.010004819}
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