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Simplifying (2x2 + 3x + 7) + -1(-4x2 + 6x + 6) + (-5x2 + 4x + -8) = 0 Reorder the terms: (7 + 3x + 2x2) + -1(-4x2 + 6x + 6) + (-5x2 + 4x + -8) = 0 Remove parenthesis around (7 + 3x + 2x2) 7 + 3x + 2x2 + -1(-4x2 + 6x + 6) + (-5x2 + 4x + -8) = 0 Reorder the terms: 7 + 3x + 2x2 + -1(6 + 6x + -4x2) + (-5x2 + 4x + -8) = 0 7 + 3x + 2x2 + (6 * -1 + 6x * -1 + -4x2 * -1) + (-5x2 + 4x + -8) = 0 7 + 3x + 2x2 + (-6 + -6x + 4x2) + (-5x2 + 4x + -8) = 0 Reorder the terms: 7 + 3x + 2x2 + -6 + -6x + 4x2 + (-8 + 4x + -5x2) = 0 Remove parenthesis around (-8 + 4x + -5x2) 7 + 3x + 2x2 + -6 + -6x + 4x2 + -8 + 4x + -5x2 = 0 Reorder the terms: 7 + -6 + -8 + 3x + -6x + 4x + 2x2 + 4x2 + -5x2 = 0 Combine like terms: 7 + -6 = 1 1 + -8 + 3x + -6x + 4x + 2x2 + 4x2 + -5x2 = 0 Combine like terms: 1 + -8 = -7 -7 + 3x + -6x + 4x + 2x2 + 4x2 + -5x2 = 0 Combine like terms: 3x + -6x = -3x -7 + -3x + 4x + 2x2 + 4x2 + -5x2 = 0 Combine like terms: -3x + 4x = 1x -7 + 1x + 2x2 + 4x2 + -5x2 = 0 Combine like terms: 2x2 + 4x2 = 6x2 -7 + 1x + 6x2 + -5x2 = 0 Combine like terms: 6x2 + -5x2 = 1x2 -7 + 1x + 1x2 = 0 Solving -7 + 1x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 1x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 1x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 1x + x2 = 0 + 7 1x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 1x + x2 = 7 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. x + 0.25 + x2 = 7 + 0.25 Reorder the terms: 0.25 + x + x2 = 7 + 0.25 Combine like terms: 7 + 0.25 = 7.25 0.25 + x + x2 = 7.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + 0.5) equal to 2.692582404 and -2.692582404.Subproblem 1
x + 0.5 = 2.692582404 Simplifying x + 0.5 = 2.692582404 Reorder the terms: 0.5 + x = 2.692582404 Solving 0.5 + x = 2.692582404 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 = 2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.692582404 + -0.5 x = 2.692582404 + -0.5 Combine like terms: 2.692582404 + -0.5 = 2.192582404 x = 2.192582404 Simplifying x = 2.192582404Subproblem 2
x + 0.5 = -2.692582404 Simplifying x + 0.5 = -2.692582404 Reorder the terms: 0.5 + x = -2.692582404 Solving 0.5 + x = -2.692582404 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 = -2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.692582404 + -0.5 x = -2.692582404 + -0.5 Combine like terms: -2.692582404 + -0.5 = -3.192582404 x = -3.192582404 Simplifying x = -3.192582404Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.192582404, -3.192582404}
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