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Simplifying 2(1 + -1x2) + -3x(1 + -1x) = 7 (1 * 2 + -1x2 * 2) + -3x(1 + -1x) = 7 (2 + -2x2) + -3x(1 + -1x) = 7 2 + -2x2 + (1 * -3x + -1x * -3x) = 7 2 + -2x2 + (-3x + 3x2) = 7 Reorder the terms: 2 + -3x + -2x2 + 3x2 = 7 Combine like terms: -2x2 + 3x2 = 1x2 2 + -3x + 1x2 = 7 Solving 2 + -3x + 1x2 = 7 Solving for variable 'x'. Reorder the terms: 2 + -7 + -3x + 1x2 = 7 + -7 Combine like terms: 2 + -7 = -5 -5 + -3x + 1x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -5 + -3x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -3x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -3x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3x + x2 = 0 + 5 -3x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -3x + x2 = 5 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 5 + 2.25 Combine like terms: 5 + 2.25 = 7.25 2.25 + -3x + x2 = 7.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + -1.5) equal to 2.692582404 and -2.692582404.Subproblem 1
x + -1.5 = 2.692582404 Simplifying x + -1.5 = 2.692582404 Reorder the terms: -1.5 + x = 2.692582404 Solving -1.5 + x = 2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.692582404 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.692582404 + 1.5 x = 2.692582404 + 1.5 Combine like terms: 2.692582404 + 1.5 = 4.192582404 x = 4.192582404 Simplifying x = 4.192582404Subproblem 2
x + -1.5 = -2.692582404 Simplifying x + -1.5 = -2.692582404 Reorder the terms: -1.5 + x = -2.692582404 Solving -1.5 + x = -2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.692582404 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.692582404 + 1.5 x = -2.692582404 + 1.5 Combine like terms: -2.692582404 + 1.5 = -1.192582404 x = -1.192582404 Simplifying x = -1.192582404Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.192582404, -1.192582404}
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