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Simplifying 2x2 + -45x = 5x2 + -4x + -30 Reorder the terms: -45x + 2x2 = 5x2 + -4x + -30 Reorder the terms: -45x + 2x2 = -30 + -4x + 5x2 Solving -45x + 2x2 = -30 + -4x + 5x2 Solving for variable 'x'. Reorder the terms: 30 + -45x + 4x + 2x2 + -5x2 = -30 + -4x + 5x2 + 30 + 4x + -5x2 Combine like terms: -45x + 4x = -41x 30 + -41x + 2x2 + -5x2 = -30 + -4x + 5x2 + 30 + 4x + -5x2 Combine like terms: 2x2 + -5x2 = -3x2 30 + -41x + -3x2 = -30 + -4x + 5x2 + 30 + 4x + -5x2 Reorder the terms: 30 + -41x + -3x2 = -30 + 30 + -4x + 4x + 5x2 + -5x2 Combine like terms: -30 + 30 = 0 30 + -41x + -3x2 = 0 + -4x + 4x + 5x2 + -5x2 30 + -41x + -3x2 = -4x + 4x + 5x2 + -5x2 Combine like terms: -4x + 4x = 0 30 + -41x + -3x2 = 0 + 5x2 + -5x2 30 + -41x + -3x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 30 + -41x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -10 + 13.66666667x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 13.66666667x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 13.66666667x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 13.66666667x + x2 = 0 + 10 13.66666667x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 13.66666667x + x2 = 10 The x term is 13.66666667x. Take half its coefficient (6.833333335). Square it (46.69444447) and add it to both sides. Add '46.69444447' to each side of the equation. 13.66666667x + 46.69444447 + x2 = 10 + 46.69444447 Reorder the terms: 46.69444447 + 13.66666667x + x2 = 10 + 46.69444447 Combine like terms: 10 + 46.69444447 = 56.69444447 46.69444447 + 13.66666667x + x2 = 56.69444447 Factor a perfect square on the left side: (x + 6.833333335)(x + 6.833333335) = 56.69444447 Calculate the square root of the right side: 7.529571334 Break this problem into two subproblems by setting (x + 6.833333335) equal to 7.529571334 and -7.529571334.Subproblem 1
x + 6.833333335 = 7.529571334 Simplifying x + 6.833333335 = 7.529571334 Reorder the terms: 6.833333335 + x = 7.529571334 Solving 6.833333335 + x = 7.529571334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.833333335' to each side of the equation. 6.833333335 + -6.833333335 + x = 7.529571334 + -6.833333335 Combine like terms: 6.833333335 + -6.833333335 = 0.000000000 0.000000000 + x = 7.529571334 + -6.833333335 x = 7.529571334 + -6.833333335 Combine like terms: 7.529571334 + -6.833333335 = 0.696237999 x = 0.696237999 Simplifying x = 0.696237999Subproblem 2
x + 6.833333335 = -7.529571334 Simplifying x + 6.833333335 = -7.529571334 Reorder the terms: 6.833333335 + x = -7.529571334 Solving 6.833333335 + x = -7.529571334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.833333335' to each side of the equation. 6.833333335 + -6.833333335 + x = -7.529571334 + -6.833333335 Combine like terms: 6.833333335 + -6.833333335 = 0.000000000 0.000000000 + x = -7.529571334 + -6.833333335 x = -7.529571334 + -6.833333335 Combine like terms: -7.529571334 + -6.833333335 = -14.362904669 x = -14.362904669 Simplifying x = -14.362904669Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.696237999, -14.362904669}
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