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Simplifying 9x2 + -50x + -39 = 0 Reorder the terms: -39 + -50x + 9x2 = 0 Solving -39 + -50x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -4.333333333 + -5.555555556x + x2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + -5.555555556x + 4.333333333 + x2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + -5.555555556x + x2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + -5.555555556x + x2 = 0 + 4.333333333 -5.555555556x + x2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 -5.555555556x + x2 = 4.333333333 The x term is -5.555555556x. Take half its coefficient (-2.777777778). Square it (7.716049384) and add it to both sides. Add '7.716049384' to each side of the equation. -5.555555556x + 7.716049384 + x2 = 4.333333333 + 7.716049384 Reorder the terms: 7.716049384 + -5.555555556x + x2 = 4.333333333 + 7.716049384 Combine like terms: 4.333333333 + 7.716049384 = 12.049382717 7.716049384 + -5.555555556x + x2 = 12.049382717 Factor a perfect square on the left side: (x + -2.777777778)(x + -2.777777778) = 12.049382717 Calculate the square root of the right side: 3.471222078 Break this problem into two subproblems by setting (x + -2.777777778) equal to 3.471222078 and -3.471222078.Subproblem 1
x + -2.777777778 = 3.471222078 Simplifying x + -2.777777778 = 3.471222078 Reorder the terms: -2.777777778 + x = 3.471222078 Solving -2.777777778 + x = 3.471222078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.777777778' to each side of the equation. -2.777777778 + 2.777777778 + x = 3.471222078 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + x = 3.471222078 + 2.777777778 x = 3.471222078 + 2.777777778 Combine like terms: 3.471222078 + 2.777777778 = 6.248999856 x = 6.248999856 Simplifying x = 6.248999856Subproblem 2
x + -2.777777778 = -3.471222078 Simplifying x + -2.777777778 = -3.471222078 Reorder the terms: -2.777777778 + x = -3.471222078 Solving -2.777777778 + x = -3.471222078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.777777778' to each side of the equation. -2.777777778 + 2.777777778 + x = -3.471222078 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + x = -3.471222078 + 2.777777778 x = -3.471222078 + 2.777777778 Combine like terms: -3.471222078 + 2.777777778 = -0.6934443 x = -0.6934443 Simplifying x = -0.6934443Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.248999856, -0.6934443}
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