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Simplifying 6x2 + -73x + 9 = 0 Reorder the terms: 9 + -73x + 6x2 = 0 Solving 9 + -73x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.5 + -12.16666667x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -12.16666667x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -12.16666667x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -12.16666667x + x2 = 0 + -1.5 -12.16666667x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -12.16666667x + x2 = -1.5 The x term is -12.16666667x. Take half its coefficient (-6.083333335). Square it (37.00694446) and add it to both sides. Add '37.00694446' to each side of the equation. -12.16666667x + 37.00694446 + x2 = -1.5 + 37.00694446 Reorder the terms: 37.00694446 + -12.16666667x + x2 = -1.5 + 37.00694446 Combine like terms: -1.5 + 37.00694446 = 35.50694446 37.00694446 + -12.16666667x + x2 = 35.50694446 Factor a perfect square on the left side: (x + -6.083333335)(x + -6.083333335) = 35.50694446 Calculate the square root of the right side: 5.958770382 Break this problem into two subproblems by setting (x + -6.083333335) equal to 5.958770382 and -5.958770382.Subproblem 1
x + -6.083333335 = 5.958770382 Simplifying x + -6.083333335 = 5.958770382 Reorder the terms: -6.083333335 + x = 5.958770382 Solving -6.083333335 + x = 5.958770382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.083333335' to each side of the equation. -6.083333335 + 6.083333335 + x = 5.958770382 + 6.083333335 Combine like terms: -6.083333335 + 6.083333335 = 0.000000000 0.000000000 + x = 5.958770382 + 6.083333335 x = 5.958770382 + 6.083333335 Combine like terms: 5.958770382 + 6.083333335 = 12.042103717 x = 12.042103717 Simplifying x = 12.042103717Subproblem 2
x + -6.083333335 = -5.958770382 Simplifying x + -6.083333335 = -5.958770382 Reorder the terms: -6.083333335 + x = -5.958770382 Solving -6.083333335 + x = -5.958770382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.083333335' to each side of the equation. -6.083333335 + 6.083333335 + x = -5.958770382 + 6.083333335 Combine like terms: -6.083333335 + 6.083333335 = 0.000000000 0.000000000 + x = -5.958770382 + 6.083333335 x = -5.958770382 + 6.083333335 Combine like terms: -5.958770382 + 6.083333335 = 0.124562953 x = 0.124562953 Simplifying x = 0.124562953Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.042103717, 0.124562953}
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