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Simplifying 36x2 + 12x + 1 = 5 Reorder the terms: 1 + 12x + 36x2 = 5 Solving 1 + 12x + 36x2 = 5 Solving for variable 'x'. Reorder the terms: 1 + -5 + 12x + 36x2 = 5 + -5 Combine like terms: 1 + -5 = -4 -4 + 12x + 36x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -4 + 12x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + 3x + 9x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + 3x + 9x2)' equal to zero and attempt to solve: Simplifying -1 + 3x + 9x2 = 0 Solving -1 + 3x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.1111111111 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.3333333333x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + 0.3333333333x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + 0.3333333333x + x2 = 0 + 0.1111111111 0.3333333333x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 0.3333333333x + x2 = 0.1111111111 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 0.1111111111 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 0.1111111111 + 0.02777777779 Combine like terms: 0.1111111111 + 0.02777777779 = 0.13888888889 0.02777777779 + 0.3333333333x + x2 = 0.13888888889 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 0.13888888889 Calculate the square root of the right side: 0.372677996 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 0.372677996 and -0.372677996.Subproblem 1
x + 0.1666666667 = 0.372677996 Simplifying x + 0.1666666667 = 0.372677996 Reorder the terms: 0.1666666667 + x = 0.372677996 Solving 0.1666666667 + x = 0.372677996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 0.372677996 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.372677996 + -0.1666666667 x = 0.372677996 + -0.1666666667 Combine like terms: 0.372677996 + -0.1666666667 = 0.2060113293 x = 0.2060113293 Simplifying x = 0.2060113293Subproblem 2
x + 0.1666666667 = -0.372677996 Simplifying x + 0.1666666667 = -0.372677996 Reorder the terms: 0.1666666667 + x = -0.372677996 Solving 0.1666666667 + x = -0.372677996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -0.372677996 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.372677996 + -0.1666666667 x = -0.372677996 + -0.1666666667 Combine like terms: -0.372677996 + -0.1666666667 = -0.5393446627 x = -0.5393446627 Simplifying x = -0.5393446627Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2060113293, -0.5393446627}Solution
x = {0.2060113293, -0.5393446627}
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