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Simplifying 9x2 + 14x + -584 = 0 Reorder the terms: -584 + 14x + 9x2 = 0 Solving -584 + 14x + 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'. -64.88888889 + 1.555555556x + x2 = 0 Move the constant term to the right: Add '64.88888889' to each side of the equation. -64.88888889 + 1.555555556x + 64.88888889 + x2 = 0 + 64.88888889 Reorder the terms: -64.88888889 + 64.88888889 + 1.555555556x + x2 = 0 + 64.88888889 Combine like terms: -64.88888889 + 64.88888889 = 0.00000000 0.00000000 + 1.555555556x + x2 = 0 + 64.88888889 1.555555556x + x2 = 0 + 64.88888889 Combine like terms: 0 + 64.88888889 = 64.88888889 1.555555556x + x2 = 64.88888889 The x term is 1.555555556x. Take half its coefficient (0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. 1.555555556x + 0.6049382720 + x2 = 64.88888889 + 0.6049382720 Reorder the terms: 0.6049382720 + 1.555555556x + x2 = 64.88888889 + 0.6049382720 Combine like terms: 64.88888889 + 0.6049382720 = 65.493827162 0.6049382720 + 1.555555556x + x2 = 65.493827162 Factor a perfect square on the left side: (x + 0.777777778)(x + 0.777777778) = 65.493827162 Calculate the square root of the right side: 8.09282566 Break this problem into two subproblems by setting (x + 0.777777778) equal to 8.09282566 and -8.09282566.Subproblem 1
x + 0.777777778 = 8.09282566 Simplifying x + 0.777777778 = 8.09282566 Reorder the terms: 0.777777778 + x = 8.09282566 Solving 0.777777778 + x = 8.09282566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = 8.09282566 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = 8.09282566 + -0.777777778 x = 8.09282566 + -0.777777778 Combine like terms: 8.09282566 + -0.777777778 = 7.315047882 x = 7.315047882 Simplifying x = 7.315047882Subproblem 2
x + 0.777777778 = -8.09282566 Simplifying x + 0.777777778 = -8.09282566 Reorder the terms: 0.777777778 + x = -8.09282566 Solving 0.777777778 + x = -8.09282566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = -8.09282566 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = -8.09282566 + -0.777777778 x = -8.09282566 + -0.777777778 Combine like terms: -8.09282566 + -0.777777778 = -8.870603438 x = -8.870603438 Simplifying x = -8.870603438Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.315047882, -8.870603438}
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