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Simplifying (x2 + 5x + -1) + (-2x2 + -2x + 5) + (-3x2 + 4) = 0 Reorder the terms: (-1 + 5x + x2) + (-2x2 + -2x + 5) + (-3x2 + 4) = 0 Remove parenthesis around (-1 + 5x + x2) -1 + 5x + x2 + (-2x2 + -2x + 5) + (-3x2 + 4) = 0 Reorder the terms: -1 + 5x + x2 + (5 + -2x + -2x2) + (-3x2 + 4) = 0 Remove parenthesis around (5 + -2x + -2x2) -1 + 5x + x2 + 5 + -2x + -2x2 + (-3x2 + 4) = 0 Reorder the terms: -1 + 5x + x2 + 5 + -2x + -2x2 + (4 + -3x2) = 0 Remove parenthesis around (4 + -3x2) -1 + 5x + x2 + 5 + -2x + -2x2 + 4 + -3x2 = 0 Reorder the terms: -1 + 5 + 4 + 5x + -2x + x2 + -2x2 + -3x2 = 0 Combine like terms: -1 + 5 = 4 4 + 4 + 5x + -2x + x2 + -2x2 + -3x2 = 0 Combine like terms: 4 + 4 = 8 8 + 5x + -2x + x2 + -2x2 + -3x2 = 0 Combine like terms: 5x + -2x = 3x 8 + 3x + x2 + -2x2 + -3x2 = 0 Combine like terms: x2 + -2x2 = -1x2 8 + 3x + -1x2 + -3x2 = 0 Combine like terms: -1x2 + -3x2 = -4x2 8 + 3x + -4x2 = 0 Solving 8 + 3x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2 + -0.75x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.75x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.75x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.75x + x2 = 0 + 2 -0.75x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.75x + x2 = 2 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 2 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 2 + 0.140625 Combine like terms: 2 + 0.140625 = 2.140625 0.140625 + -0.75x + x2 = 2.140625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (x + -0.375) equal to 1.463087489 and -1.463087489.Subproblem 1
x + -0.375 = 1.463087489 Simplifying x + -0.375 = 1.463087489 Reorder the terms: -0.375 + x = 1.463087489 Solving -0.375 + x = 1.463087489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 1.463087489 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 1.463087489 + 0.375 x = 1.463087489 + 0.375 Combine like terms: 1.463087489 + 0.375 = 1.838087489 x = 1.838087489 Simplifying x = 1.838087489Subproblem 2
x + -0.375 = -1.463087489 Simplifying x + -0.375 = -1.463087489 Reorder the terms: -0.375 + x = -1.463087489 Solving -0.375 + x = -1.463087489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -1.463087489 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -1.463087489 + 0.375 x = -1.463087489 + 0.375 Combine like terms: -1.463087489 + 0.375 = -1.088087489 x = -1.088087489 Simplifying x = -1.088087489Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.838087489, -1.088087489}
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