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Simplifying (x + -1)(x + -5) = 7(x + 8) Reorder the terms: (-1 + x)(x + -5) = 7(x + 8) Reorder the terms: (-1 + x)(-5 + x) = 7(x + 8) Multiply (-1 + x) * (-5 + x) (-1(-5 + x) + x(-5 + x)) = 7(x + 8) ((-5 * -1 + x * -1) + x(-5 + x)) = 7(x + 8) ((5 + -1x) + x(-5 + x)) = 7(x + 8) (5 + -1x + (-5 * x + x * x)) = 7(x + 8) (5 + -1x + (-5x + x2)) = 7(x + 8) Combine like terms: -1x + -5x = -6x (5 + -6x + x2) = 7(x + 8) Reorder the terms: 5 + -6x + x2 = 7(8 + x) 5 + -6x + x2 = (8 * 7 + x * 7) 5 + -6x + x2 = (56 + 7x) Solving 5 + -6x + x2 = 56 + 7x Solving for variable 'x'. Reorder the terms: 5 + -56 + -6x + -7x + x2 = 56 + 7x + -56 + -7x Combine like terms: 5 + -56 = -51 -51 + -6x + -7x + x2 = 56 + 7x + -56 + -7x Combine like terms: -6x + -7x = -13x -51 + -13x + x2 = 56 + 7x + -56 + -7x Reorder the terms: -51 + -13x + x2 = 56 + -56 + 7x + -7x Combine like terms: 56 + -56 = 0 -51 + -13x + x2 = 0 + 7x + -7x -51 + -13x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -51 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + -13x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + -13x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + -13x + x2 = 0 + 51 -13x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 -13x + x2 = 51 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 51 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 51 + 42.25 Combine like terms: 51 + 42.25 = 93.25 42.25 + -13x + x2 = 93.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 93.25 Calculate the square root of the right side: 9.656603958 Break this problem into two subproblems by setting (x + -6.5) equal to 9.656603958 and -9.656603958.Subproblem 1
x + -6.5 = 9.656603958 Simplifying x + -6.5 = 9.656603958 Reorder the terms: -6.5 + x = 9.656603958 Solving -6.5 + x = 9.656603958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 9.656603958 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 9.656603958 + 6.5 x = 9.656603958 + 6.5 Combine like terms: 9.656603958 + 6.5 = 16.156603958 x = 16.156603958 Simplifying x = 16.156603958Subproblem 2
x + -6.5 = -9.656603958 Simplifying x + -6.5 = -9.656603958 Reorder the terms: -6.5 + x = -9.656603958 Solving -6.5 + x = -9.656603958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -9.656603958 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -9.656603958 + 6.5 x = -9.656603958 + 6.5 Combine like terms: -9.656603958 + 6.5 = -3.156603958 x = -3.156603958 Simplifying x = -3.156603958Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.156603958, -3.156603958}
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