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Simplifying X2 + 5xy + 6y2 = (x + 1)(x + 6) Reorder the terms: X2 + 5xy + 6y2 = (1 + x)(x + 6) Reorder the terms: X2 + 5xy + 6y2 = (1 + x)(6 + x) Multiply (1 + x) * (6 + x) X2 + 5xy + 6y2 = (1(6 + x) + x(6 + x)) X2 + 5xy + 6y2 = ((6 * 1 + x * 1) + x(6 + x)) X2 + 5xy + 6y2 = ((6 + 1x) + x(6 + x)) X2 + 5xy + 6y2 = (6 + 1x + (6 * x + x * x)) X2 + 5xy + 6y2 = (6 + 1x + (6x + x2)) Combine like terms: 1x + 6x = 7x X2 + 5xy + 6y2 = (6 + 7x + x2) Solving X2 + 5xy + 6y2 = 6 + 7x + x2 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-5xy' to each side of the equation. X2 + 5xy + -5xy + 6y2 = 6 + 7x + -5xy + x2 Combine like terms: 5xy + -5xy = 0 X2 + 0 + 6y2 = 6 + 7x + -5xy + x2 X2 + 6y2 = 6 + 7x + -5xy + x2 Add '-6y2' to each side of the equation. X2 + 6y2 + -6y2 = 6 + 7x + -5xy + x2 + -6y2 Combine like terms: 6y2 + -6y2 = 0 X2 + 0 = 6 + 7x + -5xy + x2 + -6y2 X2 = 6 + 7x + -5xy + x2 + -6y2 Simplifying X2 = 6 + 7x + -5xy + x2 + -6y2 Reorder the terms: -6 + X2 + -7x + 5xy + -1x2 + 6y2 = 6 + 7x + -5xy + x2 + -6y2 + -6 + -7x + 5xy + -1x2 + 6y2 Reorder the terms: -6 + X2 + -7x + 5xy + -1x2 + 6y2 = 6 + -6 + 7x + -7x + -5xy + 5xy + x2 + -1x2 + -6y2 + 6y2 Combine like terms: 6 + -6 = 0 -6 + X2 + -7x + 5xy + -1x2 + 6y2 = 0 + 7x + -7x + -5xy + 5xy + x2 + -1x2 + -6y2 + 6y2 -6 + X2 + -7x + 5xy + -1x2 + 6y2 = 7x + -7x + -5xy + 5xy + x2 + -1x2 + -6y2 + 6y2 Combine like terms: 7x + -7x = 0 -6 + X2 + -7x + 5xy + -1x2 + 6y2 = 0 + -5xy + 5xy + x2 + -1x2 + -6y2 + 6y2 -6 + X2 + -7x + 5xy + -1x2 + 6y2 = -5xy + 5xy + x2 + -1x2 + -6y2 + 6y2 Combine like terms: -5xy + 5xy = 0 -6 + X2 + -7x + 5xy + -1x2 + 6y2 = 0 + x2 + -1x2 + -6y2 + 6y2 -6 + X2 + -7x + 5xy + -1x2 + 6y2 = x2 + -1x2 + -6y2 + 6y2 Combine like terms: x2 + -1x2 = 0 -6 + X2 + -7x + 5xy + -1x2 + 6y2 = 0 + -6y2 + 6y2 -6 + X2 + -7x + 5xy + -1x2 + 6y2 = -6y2 + 6y2 Combine like terms: -6y2 + 6y2 = 0 -6 + X2 + -7x + 5xy + -1x2 + 6y2 = 0 The solution to this equation could not be determined.
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