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Simplifying (x + -5)(x + 3) = 7 Reorder the terms: (-5 + x)(x + 3) = 7 Reorder the terms: (-5 + x)(3 + x) = 7 Multiply (-5 + x) * (3 + x) (-5(3 + x) + x(3 + x)) = 7 ((3 * -5 + x * -5) + x(3 + x)) = 7 ((-15 + -5x) + x(3 + x)) = 7 (-15 + -5x + (3 * x + x * x)) = 7 (-15 + -5x + (3x + x2)) = 7 Combine like terms: -5x + 3x = -2x (-15 + -2x + x2) = 7 Solving -15 + -2x + x2 = 7 Solving for variable 'x'. Reorder the terms: -15 + -7 + -2x + x2 = 7 + -7 Combine like terms: -15 + -7 = -22 -22 + -2x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -22 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -2x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + -2x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -2x + x2 = 0 + 22 -2x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 -2x + x2 = 22 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 = 22 + 1 Reorder the terms: 1 + -2x + x2 = 22 + 1 Combine like terms: 22 + 1 = 23 1 + -2x + x2 = 23 Factor a perfect square on the left side: (x + -1)(x + -1) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + -1) equal to 4.795831523 and -4.795831523.Subproblem 1
x + -1 = 4.795831523 Simplifying x + -1 = 4.795831523 Reorder the terms: -1 + x = 4.795831523 Solving -1 + x = 4.795831523 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 = 4.795831523 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.795831523 + 1 x = 4.795831523 + 1 Combine like terms: 4.795831523 + 1 = 5.795831523 x = 5.795831523 Simplifying x = 5.795831523Subproblem 2
x + -1 = -4.795831523 Simplifying x + -1 = -4.795831523 Reorder the terms: -1 + x = -4.795831523 Solving -1 + x = -4.795831523 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 = -4.795831523 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.795831523 + 1 x = -4.795831523 + 1 Combine like terms: -4.795831523 + 1 = -3.795831523 x = -3.795831523 Simplifying x = -3.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.795831523, -3.795831523}
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