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Simplifying (4x2 + -6x + -34) + (5x2 + 8x) = 0 Reorder the terms: (-34 + -6x + 4x2) + (5x2 + 8x) = 0 Remove parenthesis around (-34 + -6x + 4x2) -34 + -6x + 4x2 + (5x2 + 8x) = 0 Reorder the terms: -34 + -6x + 4x2 + (8x + 5x2) = 0 Remove parenthesis around (8x + 5x2) -34 + -6x + 4x2 + 8x + 5x2 = 0 Reorder the terms: -34 + -6x + 8x + 4x2 + 5x2 = 0 Combine like terms: -6x + 8x = 2x -34 + 2x + 4x2 + 5x2 = 0 Combine like terms: 4x2 + 5x2 = 9x2 -34 + 2x + 9x2 = 0 Solving -34 + 2x + 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'. -3.777777778 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '3.777777778' to each side of the equation. -3.777777778 + 0.2222222222x + 3.777777778 + x2 = 0 + 3.777777778 Reorder the terms: -3.777777778 + 3.777777778 + 0.2222222222x + x2 = 0 + 3.777777778 Combine like terms: -3.777777778 + 3.777777778 = 0.000000000 0.000000000 + 0.2222222222x + x2 = 0 + 3.777777778 0.2222222222x + x2 = 0 + 3.777777778 Combine like terms: 0 + 3.777777778 = 3.777777778 0.2222222222x + x2 = 3.777777778 The x term is 0.2222222222x. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222x + 0.01234567901 + x2 = 3.777777778 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 3.777777778 + 0.01234567901 Combine like terms: 3.777777778 + 0.01234567901 = 3.79012345701 0.01234567901 + 0.2222222222x + x2 = 3.79012345701 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 3.79012345701 Calculate the square root of the right side: 1.946823941 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 1.946823941 and -1.946823941.Subproblem 1
x + 0.1111111111 = 1.946823941 Simplifying x + 0.1111111111 = 1.946823941 Reorder the terms: 0.1111111111 + x = 1.946823941 Solving 0.1111111111 + x = 1.946823941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = 1.946823941 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 1.946823941 + -0.1111111111 x = 1.946823941 + -0.1111111111 Combine like terms: 1.946823941 + -0.1111111111 = 1.8357128299 x = 1.8357128299 Simplifying x = 1.8357128299Subproblem 2
x + 0.1111111111 = -1.946823941 Simplifying x + 0.1111111111 = -1.946823941 Reorder the terms: 0.1111111111 + x = -1.946823941 Solving 0.1111111111 + x = -1.946823941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = -1.946823941 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -1.946823941 + -0.1111111111 x = -1.946823941 + -0.1111111111 Combine like terms: -1.946823941 + -0.1111111111 = -2.0579350521 x = -2.0579350521 Simplifying x = -2.0579350521Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8357128299, -2.0579350521}
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