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Simplifying (x + 7)(x + -3) = (x + 1) Reorder the terms: (7 + x)(x + -3) = (x + 1) Reorder the terms: (7 + x)(-3 + x) = (x + 1) Multiply (7 + x) * (-3 + x) (7(-3 + x) + x(-3 + x)) = (x + 1) ((-3 * 7 + x * 7) + x(-3 + x)) = (x + 1) ((-21 + 7x) + x(-3 + x)) = (x + 1) (-21 + 7x + (-3 * x + x * x)) = (x + 1) (-21 + 7x + (-3x + x2)) = (x + 1) Combine like terms: 7x + -3x = 4x (-21 + 4x + x2) = (x + 1) Reorder the terms: -21 + 4x + x2 = (1 + x) Remove parenthesis around (1 + x) -21 + 4x + x2 = 1 + x Solving -21 + 4x + x2 = 1 + x Solving for variable 'x'. Reorder the terms: -21 + -1 + 4x + -1x + x2 = 1 + x + -1 + -1x Combine like terms: -21 + -1 = -22 -22 + 4x + -1x + x2 = 1 + x + -1 + -1x Combine like terms: 4x + -1x = 3x -22 + 3x + x2 = 1 + x + -1 + -1x Reorder the terms: -22 + 3x + x2 = 1 + -1 + x + -1x Combine like terms: 1 + -1 = 0 -22 + 3x + x2 = 0 + x + -1x -22 + 3x + x2 = x + -1x Combine like terms: x + -1x = 0 -22 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 3x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 3x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 3x + x2 = 0 + 22 3x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 3x + x2 = 22 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 = 22 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 22 + 2.25 Combine like terms: 22 + 2.25 = 24.25 2.25 + 3x + x2 = 24.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x + 1.5) equal to 4.924428901 and -4.924428901.Subproblem 1
x + 1.5 = 4.924428901 Simplifying x + 1.5 = 4.924428901 Reorder the terms: 1.5 + x = 4.924428901 Solving 1.5 + x = 4.924428901 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 = 4.924428901 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.924428901 + -1.5 x = 4.924428901 + -1.5 Combine like terms: 4.924428901 + -1.5 = 3.424428901 x = 3.424428901 Simplifying x = 3.424428901Subproblem 2
x + 1.5 = -4.924428901 Simplifying x + 1.5 = -4.924428901 Reorder the terms: 1.5 + x = -4.924428901 Solving 1.5 + x = -4.924428901 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 = -4.924428901 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.924428901 + -1.5 x = -4.924428901 + -1.5 Combine like terms: -4.924428901 + -1.5 = -6.424428901 x = -6.424428901 Simplifying x = -6.424428901Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.424428901, -6.424428901}
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