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Simplifying (2x2 + -4x + -8) + -1(x2 + -5x + 3) = 0 Reorder the terms: (-8 + -4x + 2x2) + -1(x2 + -5x + 3) = 0 Remove parenthesis around (-8 + -4x + 2x2) -8 + -4x + 2x2 + -1(x2 + -5x + 3) = 0 Reorder the terms: -8 + -4x + 2x2 + -1(3 + -5x + x2) = 0 -8 + -4x + 2x2 + (3 * -1 + -5x * -1 + x2 * -1) = 0 -8 + -4x + 2x2 + (-3 + 5x + -1x2) = 0 Reorder the terms: -8 + -3 + -4x + 5x + 2x2 + -1x2 = 0 Combine like terms: -8 + -3 = -11 -11 + -4x + 5x + 2x2 + -1x2 = 0 Combine like terms: -4x + 5x = 1x -11 + 1x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 -11 + 1x + 1x2 = 0 Solving -11 + 1x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 1x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 1x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 1x + x2 = 0 + 11 1x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 1x + x2 = 11 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 = 11 + 0.25 Reorder the terms: 0.25 + x + x2 = 11 + 0.25 Combine like terms: 11 + 0.25 = 11.25 0.25 + x + x2 = 11.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + 0.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x + 0.5 = 3.354101966 Simplifying x + 0.5 = 3.354101966 Reorder the terms: 0.5 + x = 3.354101966 Solving 0.5 + x = 3.354101966 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 = 3.354101966 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.354101966 + -0.5 x = 3.354101966 + -0.5 Combine like terms: 3.354101966 + -0.5 = 2.854101966 x = 2.854101966 Simplifying x = 2.854101966Subproblem 2
x + 0.5 = -3.354101966 Simplifying x + 0.5 = -3.354101966 Reorder the terms: 0.5 + x = -3.354101966 Solving 0.5 + x = -3.354101966 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 = -3.354101966 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.354101966 + -0.5 x = -3.354101966 + -0.5 Combine like terms: -3.354101966 + -0.5 = -3.854101966 x = -3.854101966 Simplifying x = -3.854101966Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.854101966, -3.854101966}
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