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Simplifying x(x + 2) = 7(x + (x + 2) + 31) Reorder the terms: x(2 + x) = 7(x + (x + 2) + 31) (2 * x + x * x) = 7(x + (x + 2) + 31) (2x + x2) = 7(x + (x + 2) + 31) Reorder the terms: 2x + x2 = 7(x + (2 + x) + 31) Remove parenthesis around (2 + x) 2x + x2 = 7(x + 2 + x + 31) Reorder the terms: 2x + x2 = 7(2 + 31 + x + x) Combine like terms: 2 + 31 = 33 2x + x2 = 7(33 + x + x) Combine like terms: x + x = 2x 2x + x2 = 7(33 + 2x) 2x + x2 = (33 * 7 + 2x * 7) 2x + x2 = (231 + 14x) Solving 2x + x2 = 231 + 14x Solving for variable 'x'. Reorder the terms: -231 + 2x + -14x + x2 = 231 + 14x + -231 + -14x Combine like terms: 2x + -14x = -12x -231 + -12x + x2 = 231 + 14x + -231 + -14x Reorder the terms: -231 + -12x + x2 = 231 + -231 + 14x + -14x Combine like terms: 231 + -231 = 0 -231 + -12x + x2 = 0 + 14x + -14x -231 + -12x + x2 = 14x + -14x Combine like terms: 14x + -14x = 0 -231 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '231' to each side of the equation. -231 + -12x + 231 + x2 = 0 + 231 Reorder the terms: -231 + 231 + -12x + x2 = 0 + 231 Combine like terms: -231 + 231 = 0 0 + -12x + x2 = 0 + 231 -12x + x2 = 0 + 231 Combine like terms: 0 + 231 = 231 -12x + x2 = 231 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 231 + 36 Reorder the terms: 36 + -12x + x2 = 231 + 36 Combine like terms: 231 + 36 = 267 36 + -12x + x2 = 267 Factor a perfect square on the left side: (x + -6)(x + -6) = 267 Calculate the square root of the right side: 16.340134638 Break this problem into two subproblems by setting (x + -6) equal to 16.340134638 and -16.340134638.Subproblem 1
x + -6 = 16.340134638 Simplifying x + -6 = 16.340134638 Reorder the terms: -6 + x = 16.340134638 Solving -6 + x = 16.340134638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 16.340134638 + 6 Combine like terms: -6 + 6 = 0 0 + x = 16.340134638 + 6 x = 16.340134638 + 6 Combine like terms: 16.340134638 + 6 = 22.340134638 x = 22.340134638 Simplifying x = 22.340134638Subproblem 2
x + -6 = -16.340134638 Simplifying x + -6 = -16.340134638 Reorder the terms: -6 + x = -16.340134638 Solving -6 + x = -16.340134638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -16.340134638 + 6 Combine like terms: -6 + 6 = 0 0 + x = -16.340134638 + 6 x = -16.340134638 + 6 Combine like terms: -16.340134638 + 6 = -10.340134638 x = -10.340134638 Simplifying x = -10.340134638Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.340134638, -10.340134638}
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