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Simplifying 5x + 9x(5x + -8 + 9) + -5x + 2 = 6x + 7 + -5x + 15x Reorder the terms: 5x + 9x(-8 + 9 + 5x) + -5x + 2 = 6x + 7 + -5x + 15x Combine like terms: -8 + 9 = 1 5x + 9x(1 + 5x) + -5x + 2 = 6x + 7 + -5x + 15x 5x + (1 * 9x + 5x * 9x) + -5x + 2 = 6x + 7 + -5x + 15x 5x + (9x + 45x2) + -5x + 2 = 6x + 7 + -5x + 15x Reorder the terms: 2 + 5x + 9x + -5x + 45x2 = 6x + 7 + -5x + 15x Combine like terms: 5x + 9x = 14x 2 + 14x + -5x + 45x2 = 6x + 7 + -5x + 15x Combine like terms: 14x + -5x = 9x 2 + 9x + 45x2 = 6x + 7 + -5x + 15x Reorder the terms: 2 + 9x + 45x2 = 7 + 6x + -5x + 15x Combine like terms: 6x + -5x = 1x 2 + 9x + 45x2 = 7 + 1x + 15x Combine like terms: 1x + 15x = 16x 2 + 9x + 45x2 = 7 + 16x Solving 2 + 9x + 45x2 = 7 + 16x Solving for variable 'x'. Reorder the terms: 2 + -7 + 9x + -16x + 45x2 = 7 + 16x + -7 + -16x Combine like terms: 2 + -7 = -5 -5 + 9x + -16x + 45x2 = 7 + 16x + -7 + -16x Combine like terms: 9x + -16x = -7x -5 + -7x + 45x2 = 7 + 16x + -7 + -16x Reorder the terms: -5 + -7x + 45x2 = 7 + -7 + 16x + -16x Combine like terms: 7 + -7 = 0 -5 + -7x + 45x2 = 0 + 16x + -16x -5 + -7x + 45x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -5 + -7x + 45x2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.1111111111 + -0.1555555556x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -0.1555555556x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -0.1555555556x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -0.1555555556x + x2 = 0 + 0.1111111111 -0.1555555556x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -0.1555555556x + x2 = 0.1111111111 The x term is -0.1555555556x. Take half its coefficient (-0.0777777778). Square it (0.006049382720) and add it to both sides. Add '0.006049382720' to each side of the equation. -0.1555555556x + 0.006049382720 + x2 = 0.1111111111 + 0.006049382720 Reorder the terms: 0.006049382720 + -0.1555555556x + x2 = 0.1111111111 + 0.006049382720 Combine like terms: 0.1111111111 + 0.006049382720 = 0.11716049382 0.006049382720 + -0.1555555556x + x2 = 0.11716049382 Factor a perfect square on the left side: (x + -0.0777777778)(x + -0.0777777778) = 0.11716049382 Calculate the square root of the right side: 0.342287151 Break this problem into two subproblems by setting (x + -0.0777777778) equal to 0.342287151 and -0.342287151.Subproblem 1
x + -0.0777777778 = 0.342287151 Simplifying x + -0.0777777778 = 0.342287151 Reorder the terms: -0.0777777778 + x = 0.342287151 Solving -0.0777777778 + x = 0.342287151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0777777778' to each side of the equation. -0.0777777778 + 0.0777777778 + x = 0.342287151 + 0.0777777778 Combine like terms: -0.0777777778 + 0.0777777778 = 0.0000000000 0.0000000000 + x = 0.342287151 + 0.0777777778 x = 0.342287151 + 0.0777777778 Combine like terms: 0.342287151 + 0.0777777778 = 0.4200649288 x = 0.4200649288 Simplifying x = 0.4200649288Subproblem 2
x + -0.0777777778 = -0.342287151 Simplifying x + -0.0777777778 = -0.342287151 Reorder the terms: -0.0777777778 + x = -0.342287151 Solving -0.0777777778 + x = -0.342287151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0777777778' to each side of the equation. -0.0777777778 + 0.0777777778 + x = -0.342287151 + 0.0777777778 Combine like terms: -0.0777777778 + 0.0777777778 = 0.0000000000 0.0000000000 + x = -0.342287151 + 0.0777777778 x = -0.342287151 + 0.0777777778 Combine like terms: -0.342287151 + 0.0777777778 = -0.2645093732 x = -0.2645093732 Simplifying x = -0.2645093732Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4200649288, -0.2645093732}
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