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Simplifying 2x2 + -8 + -1x2 + -1x + -2 + -4x + 3 = 0 Reorder the terms: -8 + -2 + 3 + -1x + -4x + 2x2 + -1x2 = 0 Combine like terms: -8 + -2 = -10 -10 + 3 + -1x + -4x + 2x2 + -1x2 = 0 Combine like terms: -10 + 3 = -7 -7 + -1x + -4x + 2x2 + -1x2 = 0 Combine like terms: -1x + -4x = -5x -7 + -5x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 -7 + -5x + 1x2 = 0 Solving -7 + -5x + 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 + -5x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -5x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5x + x2 = 0 + 7 -5x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -5x + x2 = 7 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 7 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 7 + 6.25 Combine like terms: 7 + 6.25 = 13.25 6.25 + -5x + x2 = 13.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x + -2.5) equal to 3.640054945 and -3.640054945.Subproblem 1
x + -2.5 = 3.640054945 Simplifying x + -2.5 = 3.640054945 Reorder the terms: -2.5 + x = 3.640054945 Solving -2.5 + x = 3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.640054945 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.640054945 + 2.5 x = 3.640054945 + 2.5 Combine like terms: 3.640054945 + 2.5 = 6.140054945 x = 6.140054945 Simplifying x = 6.140054945Subproblem 2
x + -2.5 = -3.640054945 Simplifying x + -2.5 = -3.640054945 Reorder the terms: -2.5 + x = -3.640054945 Solving -2.5 + x = -3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.640054945 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.640054945 + 2.5 x = -3.640054945 + 2.5 Combine like terms: -3.640054945 + 2.5 = -1.140054945 x = -1.140054945 Simplifying x = -1.140054945Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.140054945, -1.140054945}
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