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Simplifying 3x2 + 5x + -2 + -1[2 + -1x2 + 2x + 5] = 0 Reorder the terms: 3x2 + 5x + -2 + -1[2 + 5 + 2x + -1x2] = 0 Combine like terms: 2 + 5 = 7 3x2 + 5x + -2 + -1[7 + 2x + -1x2] = 0 3x2 + 5x + -2 + [7 * -1 + 2x * -1 + -1x2 * -1] = 0 3x2 + 5x + -2 + [-7 + -2x + 1x2] = 0 Reorder the terms: -2 + -7 + 5x + -2x + 3x2 + 1x2 = 0 Combine like terms: -2 + -7 = -9 -9 + 5x + -2x + 3x2 + 1x2 = 0 Combine like terms: 5x + -2x = 3x -9 + 3x + 3x2 + 1x2 = 0 Combine like terms: 3x2 + 1x2 = 4x2 -9 + 3x + 4x2 = 0 Solving -9 + 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'. -2.25 + 0.75x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 0.75x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 0.75x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 0.75x + x2 = 0 + 2.25 0.75x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 0.75x + x2 = 2.25 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 = 2.25 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 2.25 + 0.140625 Combine like terms: 2.25 + 0.140625 = 2.390625 0.140625 + 0.75x + x2 = 2.390625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (x + 0.375) equal to 1.54616461 and -1.54616461.Subproblem 1
x + 0.375 = 1.54616461 Simplifying x + 0.375 = 1.54616461 Reorder the terms: 0.375 + x = 1.54616461 Solving 0.375 + x = 1.54616461 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 = 1.54616461 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.54616461 + -0.375 x = 1.54616461 + -0.375 Combine like terms: 1.54616461 + -0.375 = 1.17116461 x = 1.17116461 Simplifying x = 1.17116461Subproblem 2
x + 0.375 = -1.54616461 Simplifying x + 0.375 = -1.54616461 Reorder the terms: 0.375 + x = -1.54616461 Solving 0.375 + x = -1.54616461 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 = -1.54616461 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.54616461 + -0.375 x = -1.54616461 + -0.375 Combine like terms: -1.54616461 + -0.375 = -1.92116461 x = -1.92116461 Simplifying x = -1.92116461Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.17116461, -1.92116461}
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