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Simplifying (x + -1)(x + -7) = 4 Reorder the terms: (-1 + x)(x + -7) = 4 Reorder the terms: (-1 + x)(-7 + x) = 4 Multiply (-1 + x) * (-7 + x) (-1(-7 + x) + x(-7 + x)) = 4 ((-7 * -1 + x * -1) + x(-7 + x)) = 4 ((7 + -1x) + x(-7 + x)) = 4 (7 + -1x + (-7 * x + x * x)) = 4 (7 + -1x + (-7x + x2)) = 4 Combine like terms: -1x + -7x = -8x (7 + -8x + x2) = 4 Solving 7 + -8x + x2 = 4 Solving for variable 'x'. Reorder the terms: 7 + -4 + -8x + x2 = 4 + -4 Combine like terms: 7 + -4 = 3 3 + -8x + x2 = 4 + -4 Combine like terms: 4 + -4 = 0 3 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -8x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -8x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8x + x2 = 0 + -3 -8x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -8x + x2 = -3 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 = -3 + 16 Reorder the terms: 16 + -8x + x2 = -3 + 16 Combine like terms: -3 + 16 = 13 16 + -8x + x2 = 13 Factor a perfect square on the left side: (x + -4)(x + -4) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + -4) equal to 3.605551275 and -3.605551275.Subproblem 1
x + -4 = 3.605551275 Simplifying x + -4 = 3.605551275 Reorder the terms: -4 + x = 3.605551275 Solving -4 + x = 3.605551275 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 = 3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.605551275 + 4 x = 3.605551275 + 4 Combine like terms: 3.605551275 + 4 = 7.605551275 x = 7.605551275 Simplifying x = 7.605551275Subproblem 2
x + -4 = -3.605551275 Simplifying x + -4 = -3.605551275 Reorder the terms: -4 + x = -3.605551275 Solving -4 + x = -3.605551275 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 = -3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.605551275 + 4 x = -3.605551275 + 4 Combine like terms: -3.605551275 + 4 = 0.394448725 x = 0.394448725 Simplifying x = 0.394448725Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.605551275, 0.394448725}
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