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Simplifying (x + -7)(x + 4) = 2(x + -1) + 4 Reorder the terms: (-7 + x)(x + 4) = 2(x + -1) + 4 Reorder the terms: (-7 + x)(4 + x) = 2(x + -1) + 4 Multiply (-7 + x) * (4 + x) (-7(4 + x) + x(4 + x)) = 2(x + -1) + 4 ((4 * -7 + x * -7) + x(4 + x)) = 2(x + -1) + 4 ((-28 + -7x) + x(4 + x)) = 2(x + -1) + 4 (-28 + -7x + (4 * x + x * x)) = 2(x + -1) + 4 (-28 + -7x + (4x + x2)) = 2(x + -1) + 4 Combine like terms: -7x + 4x = -3x (-28 + -3x + x2) = 2(x + -1) + 4 Reorder the terms: -28 + -3x + x2 = 2(-1 + x) + 4 -28 + -3x + x2 = (-1 * 2 + x * 2) + 4 -28 + -3x + x2 = (-2 + 2x) + 4 Reorder the terms: -28 + -3x + x2 = -2 + 4 + 2x Combine like terms: -2 + 4 = 2 -28 + -3x + x2 = 2 + 2x Solving -28 + -3x + x2 = 2 + 2x Solving for variable 'x'. Reorder the terms: -28 + -2 + -3x + -2x + x2 = 2 + 2x + -2 + -2x Combine like terms: -28 + -2 = -30 -30 + -3x + -2x + x2 = 2 + 2x + -2 + -2x Combine like terms: -3x + -2x = -5x -30 + -5x + x2 = 2 + 2x + -2 + -2x Reorder the terms: -30 + -5x + x2 = 2 + -2 + 2x + -2x Combine like terms: 2 + -2 = 0 -30 + -5x + x2 = 0 + 2x + -2x -30 + -5x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -30 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -5x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -5x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -5x + x2 = 0 + 30 -5x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -5x + x2 = 30 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 30 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 30 + 6.25 Combine like terms: 30 + 6.25 = 36.25 6.25 + -5x + x2 = 36.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x + -2.5) equal to 6.020797289 and -6.020797289.Subproblem 1
x + -2.5 = 6.020797289 Simplifying x + -2.5 = 6.020797289 Reorder the terms: -2.5 + x = 6.020797289 Solving -2.5 + x = 6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 6.020797289 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 6.020797289 + 2.5 x = 6.020797289 + 2.5 Combine like terms: 6.020797289 + 2.5 = 8.520797289 x = 8.520797289 Simplifying x = 8.520797289Subproblem 2
x + -2.5 = -6.020797289 Simplifying x + -2.5 = -6.020797289 Reorder the terms: -2.5 + x = -6.020797289 Solving -2.5 + x = -6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -6.020797289 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -6.020797289 + 2.5 x = -6.020797289 + 2.5 Combine like terms: -6.020797289 + 2.5 = -3.520797289 x = -3.520797289 Simplifying x = -3.520797289Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.520797289, -3.520797289}
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