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Simplifying -3x2 + 340x + 16200 = 0 Reorder the terms: 16200 + 340x + -3x2 = 0 Solving 16200 + 340x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -5400 + -113.3333333x + x2 = 0 Move the constant term to the right: Add '5400' to each side of the equation. -5400 + -113.3333333x + 5400 + x2 = 0 + 5400 Reorder the terms: -5400 + 5400 + -113.3333333x + x2 = 0 + 5400 Combine like terms: -5400 + 5400 = 0 0 + -113.3333333x + x2 = 0 + 5400 -113.3333333x + x2 = 0 + 5400 Combine like terms: 0 + 5400 = 5400 -113.3333333x + x2 = 5400 The x term is -113.3333333x. Take half its coefficient (-56.66666665). Square it (3211.111109) and add it to both sides. Add '3211.111109' to each side of the equation. -113.3333333x + 3211.111109 + x2 = 5400 + 3211.111109 Reorder the terms: 3211.111109 + -113.3333333x + x2 = 5400 + 3211.111109 Combine like terms: 5400 + 3211.111109 = 8611.111109 3211.111109 + -113.3333333x + x2 = 8611.111109 Factor a perfect square on the left side: (x + -56.66666665)(x + -56.66666665) = 8611.111109 Calculate the square root of the right side: 92.796072702 Break this problem into two subproblems by setting (x + -56.66666665) equal to 92.796072702 and -92.796072702.Subproblem 1
x + -56.66666665 = 92.796072702 Simplifying x + -56.66666665 = 92.796072702 Reorder the terms: -56.66666665 + x = 92.796072702 Solving -56.66666665 + x = 92.796072702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56.66666665' to each side of the equation. -56.66666665 + 56.66666665 + x = 92.796072702 + 56.66666665 Combine like terms: -56.66666665 + 56.66666665 = 0.00000000 0.00000000 + x = 92.796072702 + 56.66666665 x = 92.796072702 + 56.66666665 Combine like terms: 92.796072702 + 56.66666665 = 149.462739352 x = 149.462739352 Simplifying x = 149.462739352Subproblem 2
x + -56.66666665 = -92.796072702 Simplifying x + -56.66666665 = -92.796072702 Reorder the terms: -56.66666665 + x = -92.796072702 Solving -56.66666665 + x = -92.796072702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56.66666665' to each side of the equation. -56.66666665 + 56.66666665 + x = -92.796072702 + 56.66666665 Combine like terms: -56.66666665 + 56.66666665 = 0.00000000 0.00000000 + x = -92.796072702 + 56.66666665 x = -92.796072702 + 56.66666665 Combine like terms: -92.796072702 + 56.66666665 = -36.129406052 x = -36.129406052 Simplifying x = -36.129406052Solution
The solution to the problem is based on the solutions from the subproblems. x = {149.462739352, -36.129406052}
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