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Simplifying (x + 7)(x + -2) = (x + 1) Reorder the terms: (7 + x)(x + -2) = (x + 1) Reorder the terms: (7 + x)(-2 + x) = (x + 1) Multiply (7 + x) * (-2 + x) (7(-2 + x) + x(-2 + x)) = (x + 1) ((-2 * 7 + x * 7) + x(-2 + x)) = (x + 1) ((-14 + 7x) + x(-2 + x)) = (x + 1) (-14 + 7x + (-2 * x + x * x)) = (x + 1) (-14 + 7x + (-2x + x2)) = (x + 1) Combine like terms: 7x + -2x = 5x (-14 + 5x + x2) = (x + 1) Reorder the terms: -14 + 5x + x2 = (1 + x) Remove parenthesis around (1 + x) -14 + 5x + x2 = 1 + x Solving -14 + 5x + x2 = 1 + x Solving for variable 'x'. Reorder the terms: -14 + -1 + 5x + -1x + x2 = 1 + x + -1 + -1x Combine like terms: -14 + -1 = -15 -15 + 5x + -1x + x2 = 1 + x + -1 + -1x Combine like terms: 5x + -1x = 4x -15 + 4x + x2 = 1 + x + -1 + -1x Reorder the terms: -15 + 4x + x2 = 1 + -1 + x + -1x Combine like terms: 1 + -1 = 0 -15 + 4x + x2 = 0 + x + -1x -15 + 4x + x2 = x + -1x Combine like terms: x + -1x = 0 -15 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 4x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 4x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 4x + x2 = 0 + 15 4x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 4x + x2 = 15 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 = 15 + 4 Reorder the terms: 4 + 4x + x2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + 4x + x2 = 19 Factor a perfect square on the left side: (x + 2)(x + 2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + 2) equal to 4.358898944 and -4.358898944.Subproblem 1
x + 2 = 4.358898944 Simplifying x + 2 = 4.358898944 Reorder the terms: 2 + x = 4.358898944 Solving 2 + x = 4.358898944 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 = 4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.358898944 + -2 x = 4.358898944 + -2 Combine like terms: 4.358898944 + -2 = 2.358898944 x = 2.358898944 Simplifying x = 2.358898944Subproblem 2
x + 2 = -4.358898944 Simplifying x + 2 = -4.358898944 Reorder the terms: 2 + x = -4.358898944 Solving 2 + x = -4.358898944 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 = -4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.358898944 + -2 x = -4.358898944 + -2 Combine like terms: -4.358898944 + -2 = -6.358898944 x = -6.358898944 Simplifying x = -6.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.358898944, -6.358898944}
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