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Simplifying (x2 + 3) + (3x2 + -1x) + -1(6 + 5x) = 0 Reorder the terms: (3 + x2) + (3x2 + -1x) + -1(6 + 5x) = 0 Remove parenthesis around (3 + x2) 3 + x2 + (3x2 + -1x) + -1(6 + 5x) = 0 Reorder the terms: 3 + x2 + (-1x + 3x2) + -1(6 + 5x) = 0 Remove parenthesis around (-1x + 3x2) 3 + x2 + -1x + 3x2 + -1(6 + 5x) = 0 3 + x2 + -1x + 3x2 + (6 * -1 + 5x * -1) = 0 3 + x2 + -1x + 3x2 + (-6 + -5x) = 0 Reorder the terms: 3 + -6 + -1x + -5x + x2 + 3x2 = 0 Combine like terms: 3 + -6 = -3 -3 + -1x + -5x + x2 + 3x2 = 0 Combine like terms: -1x + -5x = -6x -3 + -6x + x2 + 3x2 = 0 Combine like terms: x2 + 3x2 = 4x2 -3 + -6x + 4x2 = 0 Solving -3 + -6x + 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'. -0.75 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.5x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.5x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.5x + x2 = 0 + 0.75 -1.5x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.5x + x2 = 0.75 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.75 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.75 + 0.5625 Combine like terms: 0.75 + 0.5625 = 1.3125 0.5625 + -1.5x + x2 = 1.3125 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 1.3125 Calculate the square root of the right side: 1.145643924 Break this problem into two subproblems by setting (x + -0.75) equal to 1.145643924 and -1.145643924.Subproblem 1
x + -0.75 = 1.145643924 Simplifying x + -0.75 = 1.145643924 Reorder the terms: -0.75 + x = 1.145643924 Solving -0.75 + x = 1.145643924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.145643924 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.145643924 + 0.75 x = 1.145643924 + 0.75 Combine like terms: 1.145643924 + 0.75 = 1.895643924 x = 1.895643924 Simplifying x = 1.895643924Subproblem 2
x + -0.75 = -1.145643924 Simplifying x + -0.75 = -1.145643924 Reorder the terms: -0.75 + x = -1.145643924 Solving -0.75 + x = -1.145643924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.145643924 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.145643924 + 0.75 x = -1.145643924 + 0.75 Combine like terms: -1.145643924 + 0.75 = -0.395643924 x = -0.395643924 Simplifying x = -0.395643924Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.895643924, -0.395643924}
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