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Simplifying (6x + 2)(6x + 2) = 50 Reorder the terms: (2 + 6x)(6x + 2) = 50 Reorder the terms: (2 + 6x)(2 + 6x) = 50 Multiply (2 + 6x) * (2 + 6x) (2(2 + 6x) + 6x * (2 + 6x)) = 50 ((2 * 2 + 6x * 2) + 6x * (2 + 6x)) = 50 ((4 + 12x) + 6x * (2 + 6x)) = 50 (4 + 12x + (2 * 6x + 6x * 6x)) = 50 (4 + 12x + (12x + 36x2)) = 50 Combine like terms: 12x + 12x = 24x (4 + 24x + 36x2) = 50 Solving 4 + 24x + 36x2 = 50 Solving for variable 'x'. Reorder the terms: 4 + -50 + 24x + 36x2 = 50 + -50 Combine like terms: 4 + -50 = -46 -46 + 24x + 36x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -46 + 24x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-23 + 12x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-23 + 12x + 18x2)' equal to zero and attempt to solve: Simplifying -23 + 12x + 18x2 = 0 Solving -23 + 12x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -1.277777778 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '1.277777778' to each side of the equation. -1.277777778 + 0.6666666667x + 1.277777778 + x2 = 0 + 1.277777778 Reorder the terms: -1.277777778 + 1.277777778 + 0.6666666667x + x2 = 0 + 1.277777778 Combine like terms: -1.277777778 + 1.277777778 = 0.000000000 0.000000000 + 0.6666666667x + x2 = 0 + 1.277777778 0.6666666667x + x2 = 0 + 1.277777778 Combine like terms: 0 + 1.277777778 = 1.277777778 0.6666666667x + x2 = 1.277777778 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 1.277777778 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 1.277777778 + 0.1111111112 Combine like terms: 1.277777778 + 0.1111111112 = 1.3888888892 0.1111111112 + 0.6666666667x + x2 = 1.3888888892 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 1.3888888892 Calculate the square root of the right side: 1.178511302 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 1.178511302 and -1.178511302.Subproblem 1
x + 0.3333333334 = 1.178511302 Simplifying x + 0.3333333334 = 1.178511302 Reorder the terms: 0.3333333334 + x = 1.178511302 Solving 0.3333333334 + x = 1.178511302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 1.178511302 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 1.178511302 + -0.3333333334 x = 1.178511302 + -0.3333333334 Combine like terms: 1.178511302 + -0.3333333334 = 0.8451779686 x = 0.8451779686 Simplifying x = 0.8451779686Subproblem 2
x + 0.3333333334 = -1.178511302 Simplifying x + 0.3333333334 = -1.178511302 Reorder the terms: 0.3333333334 + x = -1.178511302 Solving 0.3333333334 + x = -1.178511302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -1.178511302 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -1.178511302 + -0.3333333334 x = -1.178511302 + -0.3333333334 Combine like terms: -1.178511302 + -0.3333333334 = -1.5118446354 x = -1.5118446354 Simplifying x = -1.5118446354Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8451779686, -1.5118446354}Solution
x = {0.8451779686, -1.5118446354}
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