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Simplifying (2x2 + -5x + 3) + (5x2 + -2x + -5) = 0 Reorder the terms: (3 + -5x + 2x2) + (5x2 + -2x + -5) = 0 Remove parenthesis around (3 + -5x + 2x2) 3 + -5x + 2x2 + (5x2 + -2x + -5) = 0 Reorder the terms: 3 + -5x + 2x2 + (-5 + -2x + 5x2) = 0 Remove parenthesis around (-5 + -2x + 5x2) 3 + -5x + 2x2 + -5 + -2x + 5x2 = 0 Reorder the terms: 3 + -5 + -5x + -2x + 2x2 + 5x2 = 0 Combine like terms: 3 + -5 = -2 -2 + -5x + -2x + 2x2 + 5x2 = 0 Combine like terms: -5x + -2x = -7x -2 + -7x + 2x2 + 5x2 = 0 Combine like terms: 2x2 + 5x2 = 7x2 -2 + -7x + 7x2 = 0 Solving -2 + -7x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + -1x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -1x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -1x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + 0.2857142857 -1x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -1x + x2 = 0.2857142857 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.2857142857 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.2857142857 + 0.25 Combine like terms: 0.2857142857 + 0.25 = 0.5357142857 0.25 + -1x + x2 = 0.5357142857 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.5357142857 Calculate the square root of the right side: 0.731925055 Break this problem into two subproblems by setting (x + -0.5) equal to 0.731925055 and -0.731925055.Subproblem 1
x + -0.5 = 0.731925055 Simplifying x + -0.5 = 0.731925055 Reorder the terms: -0.5 + x = 0.731925055 Solving -0.5 + x = 0.731925055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.731925055 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.731925055 + 0.5 x = 0.731925055 + 0.5 Combine like terms: 0.731925055 + 0.5 = 1.231925055 x = 1.231925055 Simplifying x = 1.231925055Subproblem 2
x + -0.5 = -0.731925055 Simplifying x + -0.5 = -0.731925055 Reorder the terms: -0.5 + x = -0.731925055 Solving -0.5 + x = -0.731925055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.731925055 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.731925055 + 0.5 x = -0.731925055 + 0.5 Combine like terms: -0.731925055 + 0.5 = -0.231925055 x = -0.231925055 Simplifying x = -0.231925055Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.231925055, -0.231925055}
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