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Simplifying (x + -13)(x + 5) + 2 = 0 Reorder the terms: (-13 + x)(x + 5) + 2 = 0 Reorder the terms: (-13 + x)(5 + x) + 2 = 0 Multiply (-13 + x) * (5 + x) (-13(5 + x) + x(5 + x)) + 2 = 0 ((5 * -13 + x * -13) + x(5 + x)) + 2 = 0 ((-65 + -13x) + x(5 + x)) + 2 = 0 (-65 + -13x + (5 * x + x * x)) + 2 = 0 (-65 + -13x + (5x + x2)) + 2 = 0 Combine like terms: -13x + 5x = -8x (-65 + -8x + x2) + 2 = 0 Reorder the terms: -65 + 2 + -8x + x2 = 0 Combine like terms: -65 + 2 = -63 -63 + -8x + x2 = 0 Solving -63 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + -8x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + -8x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + -8x + x2 = 0 + 63 -8x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 -8x + x2 = 63 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 63 + 16 Reorder the terms: 16 + -8x + x2 = 63 + 16 Combine like terms: 63 + 16 = 79 16 + -8x + x2 = 79 Factor a perfect square on the left side: (x + -4)(x + -4) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (x + -4) equal to 8.888194417 and -8.888194417.Subproblem 1
x + -4 = 8.888194417 Simplifying x + -4 = 8.888194417 Reorder the terms: -4 + x = 8.888194417 Solving -4 + x = 8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 8.888194417 + 4 Combine like terms: -4 + 4 = 0 0 + x = 8.888194417 + 4 x = 8.888194417 + 4 Combine like terms: 8.888194417 + 4 = 12.888194417 x = 12.888194417 Simplifying x = 12.888194417Subproblem 2
x + -4 = -8.888194417 Simplifying x + -4 = -8.888194417 Reorder the terms: -4 + x = -8.888194417 Solving -4 + x = -8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -8.888194417 + 4 Combine like terms: -4 + 4 = 0 0 + x = -8.888194417 + 4 x = -8.888194417 + 4 Combine like terms: -8.888194417 + 4 = -4.888194417 x = -4.888194417 Simplifying x = -4.888194417Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.888194417, -4.888194417}
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