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Simplifying (6x2 + -3x + -2) + (-4x2 + -6x + -4) + -1(-3x2 + 6x + -5) = 0 Reorder the terms: (-2 + -3x + 6x2) + (-4x2 + -6x + -4) + -1(-3x2 + 6x + -5) = 0 Remove parenthesis around (-2 + -3x + 6x2) -2 + -3x + 6x2 + (-4x2 + -6x + -4) + -1(-3x2 + 6x + -5) = 0 Reorder the terms: -2 + -3x + 6x2 + (-4 + -6x + -4x2) + -1(-3x2 + 6x + -5) = 0 Remove parenthesis around (-4 + -6x + -4x2) -2 + -3x + 6x2 + -4 + -6x + -4x2 + -1(-3x2 + 6x + -5) = 0 Reorder the terms: -2 + -3x + 6x2 + -4 + -6x + -4x2 + -1(-5 + 6x + -3x2) = 0 -2 + -3x + 6x2 + -4 + -6x + -4x2 + (-5 * -1 + 6x * -1 + -3x2 * -1) = 0 -2 + -3x + 6x2 + -4 + -6x + -4x2 + (5 + -6x + 3x2) = 0 Reorder the terms: -2 + -4 + 5 + -3x + -6x + -6x + 6x2 + -4x2 + 3x2 = 0 Combine like terms: -2 + -4 = -6 -6 + 5 + -3x + -6x + -6x + 6x2 + -4x2 + 3x2 = 0 Combine like terms: -6 + 5 = -1 -1 + -3x + -6x + -6x + 6x2 + -4x2 + 3x2 = 0 Combine like terms: -3x + -6x = -9x -1 + -9x + -6x + 6x2 + -4x2 + 3x2 = 0 Combine like terms: -9x + -6x = -15x -1 + -15x + 6x2 + -4x2 + 3x2 = 0 Combine like terms: 6x2 + -4x2 = 2x2 -1 + -15x + 2x2 + 3x2 = 0 Combine like terms: 2x2 + 3x2 = 5x2 -1 + -15x + 5x2 = 0 Solving -1 + -15x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -3x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -3x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -3x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -3x + x2 = 0 + 0.2 -3x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -3x + x2 = 0.2 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 = 0.2 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.2 + 2.25 Combine like terms: 0.2 + 2.25 = 2.45 2.25 + -3x + x2 = 2.45 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.45 Calculate the square root of the right side: 1.565247584 Break this problem into two subproblems by setting (x + -1.5) equal to 1.565247584 and -1.565247584.Subproblem 1
x + -1.5 = 1.565247584 Simplifying x + -1.5 = 1.565247584 Reorder the terms: -1.5 + x = 1.565247584 Solving -1.5 + x = 1.565247584 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 = 1.565247584 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.565247584 + 1.5 x = 1.565247584 + 1.5 Combine like terms: 1.565247584 + 1.5 = 3.065247584 x = 3.065247584 Simplifying x = 3.065247584Subproblem 2
x + -1.5 = -1.565247584 Simplifying x + -1.5 = -1.565247584 Reorder the terms: -1.5 + x = -1.565247584 Solving -1.5 + x = -1.565247584 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 = -1.565247584 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.565247584 + 1.5 x = -1.565247584 + 1.5 Combine like terms: -1.565247584 + 1.5 = -0.065247584 x = -0.065247584 Simplifying x = -0.065247584Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.065247584, -0.065247584}
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