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Simplifying (2x + 1)(x + 5) = 6x Reorder the terms: (1 + 2x)(x + 5) = 6x Reorder the terms: (1 + 2x)(5 + x) = 6x Multiply (1 + 2x) * (5 + x) (1(5 + x) + 2x * (5 + x)) = 6x ((5 * 1 + x * 1) + 2x * (5 + x)) = 6x ((5 + 1x) + 2x * (5 + x)) = 6x (5 + 1x + (5 * 2x + x * 2x)) = 6x (5 + 1x + (10x + 2x2)) = 6x Combine like terms: 1x + 10x = 11x (5 + 11x + 2x2) = 6x Solving 5 + 11x + 2x2 = 6x Solving for variable 'x'. Reorder the terms: 5 + 11x + -6x + 2x2 = 6x + -6x Combine like terms: 11x + -6x = 5x 5 + 5x + 2x2 = 6x + -6x Combine like terms: 6x + -6x = 0 5 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 2.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 2.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 2.5x + x2 = 0 + -2.5 2.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 2.5x + x2 = -2.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = -2.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -2.5 + 1.5625 Combine like terms: -2.5 + 1.5625 = -0.9375 1.5625 + 2.5x + x2 = -0.9375 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = -0.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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