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Simplifying (3x2 + -2x + 7) + (x2 + 5x + -11) = 0 Reorder the terms: (7 + -2x + 3x2) + (x2 + 5x + -11) = 0 Remove parenthesis around (7 + -2x + 3x2) 7 + -2x + 3x2 + (x2 + 5x + -11) = 0 Reorder the terms: 7 + -2x + 3x2 + (-11 + 5x + x2) = 0 Remove parenthesis around (-11 + 5x + x2) 7 + -2x + 3x2 + -11 + 5x + x2 = 0 Reorder the terms: 7 + -11 + -2x + 5x + 3x2 + x2 = 0 Combine like terms: 7 + -11 = -4 -4 + -2x + 5x + 3x2 + x2 = 0 Combine like terms: -2x + 5x = 3x -4 + 3x + 3x2 + x2 = 0 Combine like terms: 3x2 + x2 = 4x2 -4 + 3x + 4x2 = 0 Solving -4 + 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'. -1 + 0.75x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.75x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.75x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.75x + x2 = 0 + 1 0.75x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.75x + x2 = 1 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 = 1 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 1 + 0.140625 Combine like terms: 1 + 0.140625 = 1.140625 0.140625 + 0.75x + x2 = 1.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (x + 0.375) equal to 1.068000468 and -1.068000468.Subproblem 1
x + 0.375 = 1.068000468 Simplifying x + 0.375 = 1.068000468 Reorder the terms: 0.375 + x = 1.068000468 Solving 0.375 + x = 1.068000468 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 = 1.068000468 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.068000468 + -0.375 x = 1.068000468 + -0.375 Combine like terms: 1.068000468 + -0.375 = 0.693000468 x = 0.693000468 Simplifying x = 0.693000468Subproblem 2
x + 0.375 = -1.068000468 Simplifying x + 0.375 = -1.068000468 Reorder the terms: 0.375 + x = -1.068000468 Solving 0.375 + x = -1.068000468 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 = -1.068000468 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.068000468 + -0.375 x = -1.068000468 + -0.375 Combine like terms: -1.068000468 + -0.375 = -1.443000468 x = -1.443000468 Simplifying x = -1.443000468Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.693000468, -1.443000468}
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