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Simplifying 1107 + -272x + 12x2 = 0 Solving 1107 + -272x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 92.25 + -22.66666667x + x2 = 0 Move the constant term to the right: Add '-92.25' to each side of the equation. 92.25 + -22.66666667x + -92.25 + x2 = 0 + -92.25 Reorder the terms: 92.25 + -92.25 + -22.66666667x + x2 = 0 + -92.25 Combine like terms: 92.25 + -92.25 = 0.00 0.00 + -22.66666667x + x2 = 0 + -92.25 -22.66666667x + x2 = 0 + -92.25 Combine like terms: 0 + -92.25 = -92.25 -22.66666667x + x2 = -92.25 The x term is -22.66666667x. Take half its coefficient (-11.33333334). Square it (128.4444446) and add it to both sides. Add '128.4444446' to each side of the equation. -22.66666667x + 128.4444446 + x2 = -92.25 + 128.4444446 Reorder the terms: 128.4444446 + -22.66666667x + x2 = -92.25 + 128.4444446 Combine like terms: -92.25 + 128.4444446 = 36.1944446 128.4444446 + -22.66666667x + x2 = 36.1944446 Factor a perfect square on the left side: (x + -11.33333334)(x + -11.33333334) = 36.1944446 Calculate the square root of the right side: 6.016181896 Break this problem into two subproblems by setting (x + -11.33333334) equal to 6.016181896 and -6.016181896.Subproblem 1
x + -11.33333334 = 6.016181896 Simplifying x + -11.33333334 = 6.016181896 Reorder the terms: -11.33333334 + x = 6.016181896 Solving -11.33333334 + x = 6.016181896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.33333334' to each side of the equation. -11.33333334 + 11.33333334 + x = 6.016181896 + 11.33333334 Combine like terms: -11.33333334 + 11.33333334 = 0.00000000 0.00000000 + x = 6.016181896 + 11.33333334 x = 6.016181896 + 11.33333334 Combine like terms: 6.016181896 + 11.33333334 = 17.349515236 x = 17.349515236 Simplifying x = 17.349515236Subproblem 2
x + -11.33333334 = -6.016181896 Simplifying x + -11.33333334 = -6.016181896 Reorder the terms: -11.33333334 + x = -6.016181896 Solving -11.33333334 + x = -6.016181896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.33333334' to each side of the equation. -11.33333334 + 11.33333334 + x = -6.016181896 + 11.33333334 Combine like terms: -11.33333334 + 11.33333334 = 0.00000000 0.00000000 + x = -6.016181896 + 11.33333334 x = -6.016181896 + 11.33333334 Combine like terms: -6.016181896 + 11.33333334 = 5.317151444 x = 5.317151444 Simplifying x = 5.317151444Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.349515236, 5.317151444}
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