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Simplifying (9x + 1)(9x + 1) = 4(x * x + -1) + x + 1 Reorder the terms: (1 + 9x)(9x + 1) = 4(x * x + -1) + x + 1 Reorder the terms: (1 + 9x)(1 + 9x) = 4(x * x + -1) + x + 1 Multiply (1 + 9x) * (1 + 9x) (1(1 + 9x) + 9x * (1 + 9x)) = 4(x * x + -1) + x + 1 ((1 * 1 + 9x * 1) + 9x * (1 + 9x)) = 4(x * x + -1) + x + 1 ((1 + 9x) + 9x * (1 + 9x)) = 4(x * x + -1) + x + 1 (1 + 9x + (1 * 9x + 9x * 9x)) = 4(x * x + -1) + x + 1 (1 + 9x + (9x + 81x2)) = 4(x * x + -1) + x + 1 Combine like terms: 9x + 9x = 18x (1 + 18x + 81x2) = 4(x * x + -1) + x + 1 Multiply x * x 1 + 18x + 81x2 = 4(x2 + -1) + x + 1 Reorder the terms: 1 + 18x + 81x2 = 4(-1 + x2) + x + 1 1 + 18x + 81x2 = (-1 * 4 + x2 * 4) + x + 1 1 + 18x + 81x2 = (-4 + 4x2) + x + 1 Reorder the terms: 1 + 18x + 81x2 = -4 + 1 + x + 4x2 Combine like terms: -4 + 1 = -3 1 + 18x + 81x2 = -3 + x + 4x2 Solving 1 + 18x + 81x2 = -3 + x + 4x2 Solving for variable 'x'. Reorder the terms: 1 + 3 + 18x + -1x + 81x2 + -4x2 = -3 + x + 4x2 + 3 + -1x + -4x2 Combine like terms: 1 + 3 = 4 4 + 18x + -1x + 81x2 + -4x2 = -3 + x + 4x2 + 3 + -1x + -4x2 Combine like terms: 18x + -1x = 17x 4 + 17x + 81x2 + -4x2 = -3 + x + 4x2 + 3 + -1x + -4x2 Combine like terms: 81x2 + -4x2 = 77x2 4 + 17x + 77x2 = -3 + x + 4x2 + 3 + -1x + -4x2 Reorder the terms: 4 + 17x + 77x2 = -3 + 3 + x + -1x + 4x2 + -4x2 Combine like terms: -3 + 3 = 0 4 + 17x + 77x2 = 0 + x + -1x + 4x2 + -4x2 4 + 17x + 77x2 = x + -1x + 4x2 + -4x2 Combine like terms: x + -1x = 0 4 + 17x + 77x2 = 0 + 4x2 + -4x2 4 + 17x + 77x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 4 + 17x + 77x2 = 0 Begin completing the square. Divide all terms by 77 the coefficient of the squared term: Divide each side by '77'. 0.05194805195 + 0.2207792208x + x2 = 0 Move the constant term to the right: Add '-0.05194805195' to each side of the equation. 0.05194805195 + 0.2207792208x + -0.05194805195 + x2 = 0 + -0.05194805195 Reorder the terms: 0.05194805195 + -0.05194805195 + 0.2207792208x + x2 = 0 + -0.05194805195 Combine like terms: 0.05194805195 + -0.05194805195 = 0.00000000000 0.00000000000 + 0.2207792208x + x2 = 0 + -0.05194805195 0.2207792208x + x2 = 0 + -0.05194805195 Combine like terms: 0 + -0.05194805195 = -0.05194805195 0.2207792208x + x2 = -0.05194805195 The x term is 0.2207792208x. Take half its coefficient (0.1103896104). Square it (0.01218586608) and add it to both sides. Add '0.01218586608' to each side of the equation. 0.2207792208x + 0.01218586608 + x2 = -0.05194805195 + 0.01218586608 Reorder the terms: 0.01218586608 + 0.2207792208x + x2 = -0.05194805195 + 0.01218586608 Combine like terms: -0.05194805195 + 0.01218586608 = -0.03976218587 0.01218586608 + 0.2207792208x + x2 = -0.03976218587 Factor a perfect square on the left side: (x + 0.1103896104)(x + 0.1103896104) = -0.03976218587 Can't calculate square root of the right side. The solution to this equation could not be determined.
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