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Simplifying (13x + 7)(13x + 7) + 50 = 0 Reorder the terms: (7 + 13x)(13x + 7) + 50 = 0 Reorder the terms: (7 + 13x)(7 + 13x) + 50 = 0 Multiply (7 + 13x) * (7 + 13x) (7(7 + 13x) + 13x * (7 + 13x)) + 50 = 0 ((7 * 7 + 13x * 7) + 13x * (7 + 13x)) + 50 = 0 ((49 + 91x) + 13x * (7 + 13x)) + 50 = 0 (49 + 91x + (7 * 13x + 13x * 13x)) + 50 = 0 (49 + 91x + (91x + 169x2)) + 50 = 0 Combine like terms: 91x + 91x = 182x (49 + 182x + 169x2) + 50 = 0 Reorder the terms: 49 + 50 + 182x + 169x2 = 0 Combine like terms: 49 + 50 = 99 99 + 182x + 169x2 = 0 Solving 99 + 182x + 169x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 169 the coefficient of the squared term: Divide each side by '169'. 0.5857988166 + 1.076923077x + x2 = 0 Move the constant term to the right: Add '-0.5857988166' to each side of the equation. 0.5857988166 + 1.076923077x + -0.5857988166 + x2 = 0 + -0.5857988166 Reorder the terms: 0.5857988166 + -0.5857988166 + 1.076923077x + x2 = 0 + -0.5857988166 Combine like terms: 0.5857988166 + -0.5857988166 = 0.0000000000 0.0000000000 + 1.076923077x + x2 = 0 + -0.5857988166 1.076923077x + x2 = 0 + -0.5857988166 Combine like terms: 0 + -0.5857988166 = -0.5857988166 1.076923077x + x2 = -0.5857988166 The x term is 1.076923077x. Take half its coefficient (0.5384615385). Square it (0.2899408284) and add it to both sides. Add '0.2899408284' to each side of the equation. 1.076923077x + 0.2899408284 + x2 = -0.5857988166 + 0.2899408284 Reorder the terms: 0.2899408284 + 1.076923077x + x2 = -0.5857988166 + 0.2899408284 Combine like terms: -0.5857988166 + 0.2899408284 = -0.2958579882 0.2899408284 + 1.076923077x + x2 = -0.2958579882 Factor a perfect square on the left side: (x + 0.5384615385)(x + 0.5384615385) = -0.2958579882 Can't calculate square root of the right side. The solution to this equation could not be determined.
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