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Simplifying (X + 4)(X + 6) = 5X + 3 Reorder the terms: (4 + X)(X + 6) = 5X + 3 Reorder the terms: (4 + X)(6 + X) = 5X + 3 Multiply (4 + X) * (6 + X) (4(6 + X) + X(6 + X)) = 5X + 3 ((6 * 4 + X * 4) + X(6 + X)) = 5X + 3 ((24 + 4X) + X(6 + X)) = 5X + 3 (24 + 4X + (6 * X + X * X)) = 5X + 3 (24 + 4X + (6X + X2)) = 5X + 3 Combine like terms: 4X + 6X = 10X (24 + 10X + X2) = 5X + 3 Reorder the terms: 24 + 10X + X2 = 3 + 5X Solving 24 + 10X + X2 = 3 + 5X Solving for variable 'X'. Reorder the terms: 24 + -3 + 10X + -5X + X2 = 3 + 5X + -3 + -5X Combine like terms: 24 + -3 = 21 21 + 10X + -5X + X2 = 3 + 5X + -3 + -5X Combine like terms: 10X + -5X = 5X 21 + 5X + X2 = 3 + 5X + -3 + -5X Reorder the terms: 21 + 5X + X2 = 3 + -3 + 5X + -5X Combine like terms: 3 + -3 = 0 21 + 5X + X2 = 0 + 5X + -5X 21 + 5X + X2 = 5X + -5X Combine like terms: 5X + -5X = 0 21 + 5X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 5X + -21 + X2 = 0 + -21 Reorder the terms: 21 + -21 + 5X + X2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 5X + X2 = 0 + -21 5X + X2 = 0 + -21 Combine like terms: 0 + -21 = -21 5X + X2 = -21 The X term is 5X. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5X + 6.25 + X2 = -21 + 6.25 Reorder the terms: 6.25 + 5X + X2 = -21 + 6.25 Combine like terms: -21 + 6.25 = -14.75 6.25 + 5X + X2 = -14.75 Factor a perfect square on the left side: (X + 2.5)(X + 2.5) = -14.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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