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Simplifying (x + 11)(x + -7) = -2 Reorder the terms: (11 + x)(x + -7) = -2 Reorder the terms: (11 + x)(-7 + x) = -2 Multiply (11 + x) * (-7 + x) (11(-7 + x) + x(-7 + x)) = -2 ((-7 * 11 + x * 11) + x(-7 + x)) = -2 ((-77 + 11x) + x(-7 + x)) = -2 (-77 + 11x + (-7 * x + x * x)) = -2 (-77 + 11x + (-7x + x2)) = -2 Combine like terms: 11x + -7x = 4x (-77 + 4x + x2) = -2 Solving -77 + 4x + x2 = -2 Solving for variable 'x'. Reorder the terms: -77 + 2 + 4x + x2 = -2 + 2 Combine like terms: -77 + 2 = -75 -75 + 4x + x2 = -2 + 2 Combine like terms: -2 + 2 = 0 -75 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + 4x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 4x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 4x + x2 = 0 + 75 4x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 4x + x2 = 75 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 = 75 + 4 Reorder the terms: 4 + 4x + x2 = 75 + 4 Combine like terms: 75 + 4 = 79 4 + 4x + x2 = 79 Factor a perfect square on the left side: (x + 2)(x + 2) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (x + 2) equal to 8.888194417 and -8.888194417.Subproblem 1
x + 2 = 8.888194417 Simplifying x + 2 = 8.888194417 Reorder the terms: 2 + x = 8.888194417 Solving 2 + x = 8.888194417 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 = 8.888194417 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.888194417 + -2 x = 8.888194417 + -2 Combine like terms: 8.888194417 + -2 = 6.888194417 x = 6.888194417 Simplifying x = 6.888194417Subproblem 2
x + 2 = -8.888194417 Simplifying x + 2 = -8.888194417 Reorder the terms: 2 + x = -8.888194417 Solving 2 + x = -8.888194417 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 = -8.888194417 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.888194417 + -2 x = -8.888194417 + -2 Combine like terms: -8.888194417 + -2 = -10.888194417 x = -10.888194417 Simplifying x = -10.888194417Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.888194417, -10.888194417}
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