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Simplifying (x + 7)(x + -3) = 5 Reorder the terms: (7 + x)(x + -3) = 5 Reorder the terms: (7 + x)(-3 + x) = 5 Multiply (7 + x) * (-3 + x) (7(-3 + x) + x(-3 + x)) = 5 ((-3 * 7 + x * 7) + x(-3 + x)) = 5 ((-21 + 7x) + x(-3 + x)) = 5 (-21 + 7x + (-3 * x + x * x)) = 5 (-21 + 7x + (-3x + x2)) = 5 Combine like terms: 7x + -3x = 4x (-21 + 4x + x2) = 5 Solving -21 + 4x + x2 = 5 Solving for variable 'x'. Reorder the terms: -21 + -5 + 4x + x2 = 5 + -5 Combine like terms: -21 + -5 = -26 -26 + 4x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -26 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 4x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + 4x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 4x + x2 = 0 + 26 4x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 4x + x2 = 26 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 26 + 4 Reorder the terms: 4 + 4x + x2 = 26 + 4 Combine like terms: 26 + 4 = 30 4 + 4x + x2 = 30 Factor a perfect square on the left side: (x + 2)(x + 2) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + 2) equal to 5.477225575 and -5.477225575.Subproblem 1
x + 2 = 5.477225575 Simplifying x + 2 = 5.477225575 Reorder the terms: 2 + x = 5.477225575 Solving 2 + x = 5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 5.477225575 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.477225575 + -2 x = 5.477225575 + -2 Combine like terms: 5.477225575 + -2 = 3.477225575 x = 3.477225575 Simplifying x = 3.477225575Subproblem 2
x + 2 = -5.477225575 Simplifying x + 2 = -5.477225575 Reorder the terms: 2 + x = -5.477225575 Solving 2 + x = -5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -5.477225575 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.477225575 + -2 x = -5.477225575 + -2 Combine like terms: -5.477225575 + -2 = -7.477225575 x = -7.477225575 Simplifying x = -7.477225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.477225575, -7.477225575}
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