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Simplifying (x + -3)(x + 5) = 5 Reorder the terms: (-3 + x)(x + 5) = 5 Reorder the terms: (-3 + x)(5 + x) = 5 Multiply (-3 + x) * (5 + x) (-3(5 + x) + x(5 + x)) = 5 ((5 * -3 + x * -3) + x(5 + x)) = 5 ((-15 + -3x) + x(5 + x)) = 5 (-15 + -3x + (5 * x + x * x)) = 5 (-15 + -3x + (5x + x2)) = 5 Combine like terms: -3x + 5x = 2x (-15 + 2x + x2) = 5 Solving -15 + 2x + x2 = 5 Solving for variable 'x'. Reorder the terms: -15 + -5 + 2x + x2 = 5 + -5 Combine like terms: -15 + -5 = -20 -20 + 2x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -20 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 2x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 2x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 2x + x2 = 0 + 20 2x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 2x + x2 = 20 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 20 + 1 Reorder the terms: 1 + 2x + x2 = 20 + 1 Combine like terms: 20 + 1 = 21 1 + 2x + x2 = 21 Factor a perfect square on the left side: (x + 1)(x + 1) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + 1) equal to 4.582575695 and -4.582575695.Subproblem 1
x + 1 = 4.582575695 Simplifying x + 1 = 4.582575695 Reorder the terms: 1 + x = 4.582575695 Solving 1 + x = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.582575695 + -1 x = 4.582575695 + -1 Combine like terms: 4.582575695 + -1 = 3.582575695 x = 3.582575695 Simplifying x = 3.582575695Subproblem 2
x + 1 = -4.582575695 Simplifying x + 1 = -4.582575695 Reorder the terms: 1 + x = -4.582575695 Solving 1 + x = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.582575695 + -1 x = -4.582575695 + -1 Combine like terms: -4.582575695 + -1 = -5.582575695 x = -5.582575695 Simplifying x = -5.582575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.582575695, -5.582575695}
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