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Simplifying (6x + 5)(6x + 5) = 2 Reorder the terms: (5 + 6x)(6x + 5) = 2 Reorder the terms: (5 + 6x)(5 + 6x) = 2 Multiply (5 + 6x) * (5 + 6x) (5(5 + 6x) + 6x * (5 + 6x)) = 2 ((5 * 5 + 6x * 5) + 6x * (5 + 6x)) = 2 ((25 + 30x) + 6x * (5 + 6x)) = 2 (25 + 30x + (5 * 6x + 6x * 6x)) = 2 (25 + 30x + (30x + 36x2)) = 2 Combine like terms: 30x + 30x = 60x (25 + 60x + 36x2) = 2 Solving 25 + 60x + 36x2 = 2 Solving for variable 'x'. Reorder the terms: 25 + -2 + 60x + 36x2 = 2 + -2 Combine like terms: 25 + -2 = 23 23 + 60x + 36x2 = 2 + -2 Combine like terms: 2 + -2 = 0 23 + 60x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 0.6388888889 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '-0.6388888889' to each side of the equation. 0.6388888889 + 1.666666667x + -0.6388888889 + x2 = 0 + -0.6388888889 Reorder the terms: 0.6388888889 + -0.6388888889 + 1.666666667x + x2 = 0 + -0.6388888889 Combine like terms: 0.6388888889 + -0.6388888889 = 0.0000000000 0.0000000000 + 1.666666667x + x2 = 0 + -0.6388888889 1.666666667x + x2 = 0 + -0.6388888889 Combine like terms: 0 + -0.6388888889 = -0.6388888889 1.666666667x + x2 = -0.6388888889 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = -0.6388888889 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = -0.6388888889 + 0.6944444447 Combine like terms: -0.6388888889 + 0.6944444447 = 0.0555555558 0.6944444447 + 1.666666667x + x2 = 0.0555555558 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 0.0555555558 Calculate the square root of the right side: 0.235702261 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 0.235702261 and -0.235702261.Subproblem 1
x + 0.8333333335 = 0.235702261 Simplifying x + 0.8333333335 = 0.235702261 Reorder the terms: 0.8333333335 + x = 0.235702261 Solving 0.8333333335 + x = 0.235702261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 0.235702261 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 0.235702261 + -0.8333333335 x = 0.235702261 + -0.8333333335 Combine like terms: 0.235702261 + -0.8333333335 = -0.5976310725 x = -0.5976310725 Simplifying x = -0.5976310725Subproblem 2
x + 0.8333333335 = -0.235702261 Simplifying x + 0.8333333335 = -0.235702261 Reorder the terms: 0.8333333335 + x = -0.235702261 Solving 0.8333333335 + x = -0.235702261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -0.235702261 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -0.235702261 + -0.8333333335 x = -0.235702261 + -0.8333333335 Combine like terms: -0.235702261 + -0.8333333335 = -1.0690355945 x = -1.0690355945 Simplifying x = -1.0690355945Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.5976310725, -1.0690355945}
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