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Simplifying (x + 4)(x + 6) + 21 = 0 Reorder the terms: (4 + x)(x + 6) + 21 = 0 Reorder the terms: (4 + x)(6 + x) + 21 = 0 Multiply (4 + x) * (6 + x) (4(6 + x) + x(6 + x)) + 21 = 0 ((6 * 4 + x * 4) + x(6 + x)) + 21 = 0 ((24 + 4x) + x(6 + x)) + 21 = 0 (24 + 4x + (6 * x + x * x)) + 21 = 0 (24 + 4x + (6x + x2)) + 21 = 0 Combine like terms: 4x + 6x = 10x (24 + 10x + x2) + 21 = 0 Reorder the terms: 24 + 21 + 10x + x2 = 0 Combine like terms: 24 + 21 = 45 45 + 10x + x2 = 0 Solving 45 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + 10x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + 10x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 10x + x2 = 0 + -45 10x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 10x + x2 = -45 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -45 + 25 Reorder the terms: 25 + 10x + x2 = -45 + 25 Combine like terms: -45 + 25 = -20 25 + 10x + x2 = -20 Factor a perfect square on the left side: (x + 5)(x + 5) = -20 Can't calculate square root of the right side. The solution to this equation could not be determined.
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