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Simplifying (x + 1)(3x + 1) = 96x2 Reorder the terms: (1 + x)(3x + 1) = 96x2 Reorder the terms: (1 + x)(1 + 3x) = 96x2 Multiply (1 + x) * (1 + 3x) (1(1 + 3x) + x(1 + 3x)) = 96x2 ((1 * 1 + 3x * 1) + x(1 + 3x)) = 96x2 ((1 + 3x) + x(1 + 3x)) = 96x2 (1 + 3x + (1 * x + 3x * x)) = 96x2 (1 + 3x + (1x + 3x2)) = 96x2 Combine like terms: 3x + 1x = 4x (1 + 4x + 3x2) = 96x2 Solving 1 + 4x + 3x2 = 96x2 Solving for variable 'x'. Combine like terms: 3x2 + -96x2 = -93x2 1 + 4x + -93x2 = 96x2 + -96x2 Combine like terms: 96x2 + -96x2 = 0 1 + 4x + -93x2 = 0 Begin completing the square. Divide all terms by -93 the coefficient of the squared term: Divide each side by '-93'. -0.01075268817 + -0.04301075269x + x2 = 0 Move the constant term to the right: Add '0.01075268817' to each side of the equation. -0.01075268817 + -0.04301075269x + 0.01075268817 + x2 = 0 + 0.01075268817 Reorder the terms: -0.01075268817 + 0.01075268817 + -0.04301075269x + x2 = 0 + 0.01075268817 Combine like terms: -0.01075268817 + 0.01075268817 = 0.00000000000 0.00000000000 + -0.04301075269x + x2 = 0 + 0.01075268817 -0.04301075269x + x2 = 0 + 0.01075268817 Combine like terms: 0 + 0.01075268817 = 0.01075268817 -0.04301075269x + x2 = 0.01075268817 The x term is -0.04301075269x. Take half its coefficient (-0.02150537635). Square it (0.0004624812120) and add it to both sides. Add '0.0004624812120' to each side of the equation. -0.04301075269x + 0.0004624812120 + x2 = 0.01075268817 + 0.0004624812120 Reorder the terms: 0.0004624812120 + -0.04301075269x + x2 = 0.01075268817 + 0.0004624812120 Combine like terms: 0.01075268817 + 0.0004624812120 = 0.011215169382 0.0004624812120 + -0.04301075269x + x2 = 0.011215169382 Factor a perfect square on the left side: (x + -0.02150537635)(x + -0.02150537635) = 0.011215169382 Calculate the square root of the right side: 0.105901697 Break this problem into two subproblems by setting (x + -0.02150537635) equal to 0.105901697 and -0.105901697.Subproblem 1
x + -0.02150537635 = 0.105901697 Simplifying x + -0.02150537635 = 0.105901697 Reorder the terms: -0.02150537635 + x = 0.105901697 Solving -0.02150537635 + x = 0.105901697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02150537635' to each side of the equation. -0.02150537635 + 0.02150537635 + x = 0.105901697 + 0.02150537635 Combine like terms: -0.02150537635 + 0.02150537635 = 0.00000000000 0.00000000000 + x = 0.105901697 + 0.02150537635 x = 0.105901697 + 0.02150537635 Combine like terms: 0.105901697 + 0.02150537635 = 0.12740707335 x = 0.12740707335 Simplifying x = 0.12740707335Subproblem 2
x + -0.02150537635 = -0.105901697 Simplifying x + -0.02150537635 = -0.105901697 Reorder the terms: -0.02150537635 + x = -0.105901697 Solving -0.02150537635 + x = -0.105901697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02150537635' to each side of the equation. -0.02150537635 + 0.02150537635 + x = -0.105901697 + 0.02150537635 Combine like terms: -0.02150537635 + 0.02150537635 = 0.00000000000 0.00000000000 + x = -0.105901697 + 0.02150537635 x = -0.105901697 + 0.02150537635 Combine like terms: -0.105901697 + 0.02150537635 = -0.08439632065 x = -0.08439632065 Simplifying x = -0.08439632065Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.12740707335, -0.08439632065}
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