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Simplifying (x + -7)(x + 5) = -2 Reorder the terms: (-7 + x)(x + 5) = -2 Reorder the terms: (-7 + x)(5 + x) = -2 Multiply (-7 + x) * (5 + x) (-7(5 + x) + x(5 + x)) = -2 ((5 * -7 + x * -7) + x(5 + x)) = -2 ((-35 + -7x) + x(5 + x)) = -2 (-35 + -7x + (5 * x + x * x)) = -2 (-35 + -7x + (5x + x2)) = -2 Combine like terms: -7x + 5x = -2x (-35 + -2x + x2) = -2 Solving -35 + -2x + x2 = -2 Solving for variable 'x'. Reorder the terms: -35 + 2 + -2x + x2 = -2 + 2 Combine like terms: -35 + 2 = -33 -33 + -2x + x2 = -2 + 2 Combine like terms: -2 + 2 = 0 -33 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + -2x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + -2x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -2x + x2 = 0 + 33 -2x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 -2x + x2 = 33 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 = 33 + 1 Reorder the terms: 1 + -2x + x2 = 33 + 1 Combine like terms: 33 + 1 = 34 1 + -2x + x2 = 34 Factor a perfect square on the left side: (x + -1)(x + -1) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + -1) equal to 5.830951895 and -5.830951895.Subproblem 1
x + -1 = 5.830951895 Simplifying x + -1 = 5.830951895 Reorder the terms: -1 + x = 5.830951895 Solving -1 + x = 5.830951895 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 = 5.830951895 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.830951895 + 1 x = 5.830951895 + 1 Combine like terms: 5.830951895 + 1 = 6.830951895 x = 6.830951895 Simplifying x = 6.830951895Subproblem 2
x + -1 = -5.830951895 Simplifying x + -1 = -5.830951895 Reorder the terms: -1 + x = -5.830951895 Solving -1 + x = -5.830951895 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 = -5.830951895 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.830951895 + 1 x = -5.830951895 + 1 Combine like terms: -5.830951895 + 1 = -4.830951895 x = -4.830951895 Simplifying x = -4.830951895Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.830951895, -4.830951895}
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