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Simplifying (x2 + 5x + 3) + -1(3x2 + -6x + 4) = 0 Reorder the terms: (3 + 5x + x2) + -1(3x2 + -6x + 4) = 0 Remove parenthesis around (3 + 5x + x2) 3 + 5x + x2 + -1(3x2 + -6x + 4) = 0 Reorder the terms: 3 + 5x + x2 + -1(4 + -6x + 3x2) = 0 3 + 5x + x2 + (4 * -1 + -6x * -1 + 3x2 * -1) = 0 3 + 5x + x2 + (-4 + 6x + -3x2) = 0 Reorder the terms: 3 + -4 + 5x + 6x + x2 + -3x2 = 0 Combine like terms: 3 + -4 = -1 -1 + 5x + 6x + x2 + -3x2 = 0 Combine like terms: 5x + 6x = 11x -1 + 11x + x2 + -3x2 = 0 Combine like terms: x2 + -3x2 = -2x2 -1 + 11x + -2x2 = 0 Solving -1 + 11x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 0.5 + -5.5x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -5.5x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -5.5x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -5.5x + x2 = 0 + -0.5 -5.5x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -5.5x + x2 = -0.5 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -0.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -0.5 + 7.5625 Combine like terms: -0.5 + 7.5625 = 7.0625 7.5625 + -5.5x + x2 = 7.0625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (x + -2.75) equal to 2.657536453 and -2.657536453.Subproblem 1
x + -2.75 = 2.657536453 Simplifying x + -2.75 = 2.657536453 Reorder the terms: -2.75 + x = 2.657536453 Solving -2.75 + x = 2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 2.657536453 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 2.657536453 + 2.75 x = 2.657536453 + 2.75 Combine like terms: 2.657536453 + 2.75 = 5.407536453 x = 5.407536453 Simplifying x = 5.407536453Subproblem 2
x + -2.75 = -2.657536453 Simplifying x + -2.75 = -2.657536453 Reorder the terms: -2.75 + x = -2.657536453 Solving -2.75 + x = -2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -2.657536453 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -2.657536453 + 2.75 x = -2.657536453 + 2.75 Combine like terms: -2.657536453 + 2.75 = 0.092463547 x = 0.092463547 Simplifying x = 0.092463547Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.407536453, 0.092463547}
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