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Simplifying (2x2 + 4x + -5) + -1(3x2 + -3x + 2) = x Reorder the terms: (-5 + 4x + 2x2) + -1(3x2 + -3x + 2) = x Remove parenthesis around (-5 + 4x + 2x2) -5 + 4x + 2x2 + -1(3x2 + -3x + 2) = x Reorder the terms: -5 + 4x + 2x2 + -1(2 + -3x + 3x2) = x -5 + 4x + 2x2 + (2 * -1 + -3x * -1 + 3x2 * -1) = x -5 + 4x + 2x2 + (-2 + 3x + -3x2) = x Reorder the terms: -5 + -2 + 4x + 3x + 2x2 + -3x2 = x Combine like terms: -5 + -2 = -7 -7 + 4x + 3x + 2x2 + -3x2 = x Combine like terms: 4x + 3x = 7x -7 + 7x + 2x2 + -3x2 = x Combine like terms: 2x2 + -3x2 = -1x2 -7 + 7x + -1x2 = x Solving -7 + 7x + -1x2 = x Solving for variable 'x'. Reorder the terms: -7 + 7x + -1x + -1x2 = x + -1x Combine like terms: 7x + -1x = 6x -7 + 6x + -1x2 = x + -1x Combine like terms: x + -1x = 0 -7 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -6x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -6x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -6x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6x + x2 = 0 + -7 -6x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -6x + x2 = -7 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -7 + 9 Reorder the terms: 9 + -6x + x2 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + -6x + x2 = 2 Factor a perfect square on the left side: (x + -3)(x + -3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -3) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -3 = 1.414213562 Simplifying x + -3 = 1.414213562 Reorder the terms: -3 + x = 1.414213562 Solving -3 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.414213562 + 3 x = 1.414213562 + 3 Combine like terms: 1.414213562 + 3 = 4.414213562 x = 4.414213562 Simplifying x = 4.414213562Subproblem 2
x + -3 = -1.414213562 Simplifying x + -3 = -1.414213562 Reorder the terms: -3 + x = -1.414213562 Solving -3 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.414213562 + 3 x = -1.414213562 + 3 Combine like terms: -1.414213562 + 3 = 1.585786438 x = 1.585786438 Simplifying x = 1.585786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.414213562, 1.585786438}
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