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Simplifying 0.291666666667x2 + -4x + -9 = 3 Reorder the terms: -9 + -4x + 0.291666666667x2 = 3 Solving -9 + -4x + 0.291666666667x2 = 3 Solving for variable 'x'. Reorder the terms: -9 + -3 + -4x + 0.291666666667x2 = 3 + -3 Combine like terms: -9 + -3 = -12 -12 + -4x + 0.291666666667x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -12 + -4x + 0.291666666667x2 = 0 Begin completing the square. Divide all terms by 0.291666666667 the coefficient of the squared term: Divide each side by '0.291666666667'. -41.14285714 + -13.71428571x + x2 = 0 Move the constant term to the right: Add '41.14285714' to each side of the equation. -41.14285714 + -13.71428571x + 41.14285714 + x2 = 0 + 41.14285714 Reorder the terms: -41.14285714 + 41.14285714 + -13.71428571x + x2 = 0 + 41.14285714 Combine like terms: -41.14285714 + 41.14285714 = 0.00000000 0.00000000 + -13.71428571x + x2 = 0 + 41.14285714 -13.71428571x + x2 = 0 + 41.14285714 Combine like terms: 0 + 41.14285714 = 41.14285714 -13.71428571x + x2 = 41.14285714 The x term is -13.71428571x. Take half its coefficient (-6.857142855). Square it (47.02040813) and add it to both sides. Add '47.02040813' to each side of the equation. -13.71428571x + 47.02040813 + x2 = 41.14285714 + 47.02040813 Reorder the terms: 47.02040813 + -13.71428571x + x2 = 41.14285714 + 47.02040813 Combine like terms: 41.14285714 + 47.02040813 = 88.16326527 47.02040813 + -13.71428571x + x2 = 88.16326527 Factor a perfect square on the left side: (x + -6.857142855)(x + -6.857142855) = 88.16326527 Calculate the square root of the right side: 9.389529555 Break this problem into two subproblems by setting (x + -6.857142855) equal to 9.389529555 and -9.389529555.Subproblem 1
x + -6.857142855 = 9.389529555 Simplifying x + -6.857142855 = 9.389529555 Reorder the terms: -6.857142855 + x = 9.389529555 Solving -6.857142855 + x = 9.389529555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.857142855' to each side of the equation. -6.857142855 + 6.857142855 + x = 9.389529555 + 6.857142855 Combine like terms: -6.857142855 + 6.857142855 = 0.000000000 0.000000000 + x = 9.389529555 + 6.857142855 x = 9.389529555 + 6.857142855 Combine like terms: 9.389529555 + 6.857142855 = 16.24667241 x = 16.24667241 Simplifying x = 16.24667241Subproblem 2
x + -6.857142855 = -9.389529555 Simplifying x + -6.857142855 = -9.389529555 Reorder the terms: -6.857142855 + x = -9.389529555 Solving -6.857142855 + x = -9.389529555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.857142855' to each side of the equation. -6.857142855 + 6.857142855 + x = -9.389529555 + 6.857142855 Combine like terms: -6.857142855 + 6.857142855 = 0.000000000 0.000000000 + x = -9.389529555 + 6.857142855 x = -9.389529555 + 6.857142855 Combine like terms: -9.389529555 + 6.857142855 = -2.5323867 x = -2.5323867 Simplifying x = -2.5323867Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.24667241, -2.5323867}
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