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Simplifying (2x + 5)(x + -4) = -2(x + 3) Reorder the terms: (5 + 2x)(x + -4) = -2(x + 3) Reorder the terms: (5 + 2x)(-4 + x) = -2(x + 3) Multiply (5 + 2x) * (-4 + x) (5(-4 + x) + 2x * (-4 + x)) = -2(x + 3) ((-4 * 5 + x * 5) + 2x * (-4 + x)) = -2(x + 3) ((-20 + 5x) + 2x * (-4 + x)) = -2(x + 3) (-20 + 5x + (-4 * 2x + x * 2x)) = -2(x + 3) (-20 + 5x + (-8x + 2x2)) = -2(x + 3) Combine like terms: 5x + -8x = -3x (-20 + -3x + 2x2) = -2(x + 3) Reorder the terms: -20 + -3x + 2x2 = -2(3 + x) -20 + -3x + 2x2 = (3 * -2 + x * -2) -20 + -3x + 2x2 = (-6 + -2x) Solving -20 + -3x + 2x2 = -6 + -2x Solving for variable 'x'. Reorder the terms: -20 + 6 + -3x + 2x + 2x2 = -6 + -2x + 6 + 2x Combine like terms: -20 + 6 = -14 -14 + -3x + 2x + 2x2 = -6 + -2x + 6 + 2x Combine like terms: -3x + 2x = -1x -14 + -1x + 2x2 = -6 + -2x + 6 + 2x Reorder the terms: -14 + -1x + 2x2 = -6 + 6 + -2x + 2x Combine like terms: -6 + 6 = 0 -14 + -1x + 2x2 = 0 + -2x + 2x -14 + -1x + 2x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -14 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7 + -0.5x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -0.5x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -0.5x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -0.5x + x2 = 0 + 7 -0.5x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -0.5x + x2 = 7 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 7 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 7 + 0.0625 Combine like terms: 7 + 0.0625 = 7.0625 0.0625 + -0.5x + x2 = 7.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (x + -0.25) equal to 2.657536453 and -2.657536453.Subproblem 1
x + -0.25 = 2.657536453 Simplifying x + -0.25 = 2.657536453 Reorder the terms: -0.25 + x = 2.657536453 Solving -0.25 + x = 2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.657536453 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.657536453 + 0.25 x = 2.657536453 + 0.25 Combine like terms: 2.657536453 + 0.25 = 2.907536453 x = 2.907536453 Simplifying x = 2.907536453Subproblem 2
x + -0.25 = -2.657536453 Simplifying x + -0.25 = -2.657536453 Reorder the terms: -0.25 + x = -2.657536453 Solving -0.25 + x = -2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.657536453 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.657536453 + 0.25 x = -2.657536453 + 0.25 Combine like terms: -2.657536453 + 0.25 = -2.407536453 x = -2.407536453 Simplifying x = -2.407536453Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.907536453, -2.407536453}
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