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Simplifying 2x(x + -4) + -1(3 + -2x) = 0 Reorder the terms: 2x(-4 + x) + -1(3 + -2x) = 0 (-4 * 2x + x * 2x) + -1(3 + -2x) = 0 (-8x + 2x2) + -1(3 + -2x) = 0 -8x + 2x2 + (3 * -1 + -2x * -1) = 0 -8x + 2x2 + (-3 + 2x) = 0 Reorder the terms: -3 + -8x + 2x + 2x2 = 0 Combine like terms: -8x + 2x = -6x -3 + -6x + 2x2 = 0 Solving -3 + -6x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -3x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -3x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -3x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -3x + x2 = 0 + 1.5 -3x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -3x + x2 = 1.5 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 = 1.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 1.5 + 2.25 Combine like terms: 1.5 + 2.25 = 3.75 2.25 + -3x + x2 = 3.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (x + -1.5) equal to 1.936491673 and -1.936491673.Subproblem 1
x + -1.5 = 1.936491673 Simplifying x + -1.5 = 1.936491673 Reorder the terms: -1.5 + x = 1.936491673 Solving -1.5 + x = 1.936491673 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 = 1.936491673 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.936491673 + 1.5 x = 1.936491673 + 1.5 Combine like terms: 1.936491673 + 1.5 = 3.436491673 x = 3.436491673 Simplifying x = 3.436491673Subproblem 2
x + -1.5 = -1.936491673 Simplifying x + -1.5 = -1.936491673 Reorder the terms: -1.5 + x = -1.936491673 Solving -1.5 + x = -1.936491673 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 = -1.936491673 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.936491673 + 1.5 x = -1.936491673 + 1.5 Combine like terms: -1.936491673 + 1.5 = -0.436491673 x = -0.436491673 Simplifying x = -0.436491673Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.436491673, -0.436491673}
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