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Simplifying 9x2 + -149x + 580 = 0 Reorder the terms: 580 + -149x + 9x2 = 0 Solving 580 + -149x + 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'. 64.44444444 + -16.55555556x + x2 = 0 Move the constant term to the right: Add '-64.44444444' to each side of the equation. 64.44444444 + -16.55555556x + -64.44444444 + x2 = 0 + -64.44444444 Reorder the terms: 64.44444444 + -64.44444444 + -16.55555556x + x2 = 0 + -64.44444444 Combine like terms: 64.44444444 + -64.44444444 = 0.00000000 0.00000000 + -16.55555556x + x2 = 0 + -64.44444444 -16.55555556x + x2 = 0 + -64.44444444 Combine like terms: 0 + -64.44444444 = -64.44444444 -16.55555556x + x2 = -64.44444444 The x term is -16.55555556x. Take half its coefficient (-8.27777778). Square it (68.52160498) and add it to both sides. Add '68.52160498' to each side of the equation. -16.55555556x + 68.52160498 + x2 = -64.44444444 + 68.52160498 Reorder the terms: 68.52160498 + -16.55555556x + x2 = -64.44444444 + 68.52160498 Combine like terms: -64.44444444 + 68.52160498 = 4.07716054 68.52160498 + -16.55555556x + x2 = 4.07716054 Factor a perfect square on the left side: (x + -8.27777778)(x + -8.27777778) = 4.07716054 Calculate the square root of the right side: 2.019197994 Break this problem into two subproblems by setting (x + -8.27777778) equal to 2.019197994 and -2.019197994.Subproblem 1
x + -8.27777778 = 2.019197994 Simplifying x + -8.27777778 = 2.019197994 Reorder the terms: -8.27777778 + x = 2.019197994 Solving -8.27777778 + x = 2.019197994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.27777778' to each side of the equation. -8.27777778 + 8.27777778 + x = 2.019197994 + 8.27777778 Combine like terms: -8.27777778 + 8.27777778 = 0.00000000 0.00000000 + x = 2.019197994 + 8.27777778 x = 2.019197994 + 8.27777778 Combine like terms: 2.019197994 + 8.27777778 = 10.296975774 x = 10.296975774 Simplifying x = 10.296975774Subproblem 2
x + -8.27777778 = -2.019197994 Simplifying x + -8.27777778 = -2.019197994 Reorder the terms: -8.27777778 + x = -2.019197994 Solving -8.27777778 + x = -2.019197994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.27777778' to each side of the equation. -8.27777778 + 8.27777778 + x = -2.019197994 + 8.27777778 Combine like terms: -8.27777778 + 8.27777778 = 0.00000000 0.00000000 + x = -2.019197994 + 8.27777778 x = -2.019197994 + 8.27777778 Combine like terms: -2.019197994 + 8.27777778 = 6.258579786 x = 6.258579786 Simplifying x = 6.258579786Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.296975774, 6.258579786}
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