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Simplifying 36x2 + 2 = 60x Reorder the terms: 2 + 36x2 = 60x Solving 2 + 36x2 = 60x Solving for variable 'x'. Reorder the terms: 2 + -60x + 36x2 = 60x + -60x Combine like terms: 60x + -60x = 0 2 + -60x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -30x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -30x + 18x2)' equal to zero and attempt to solve: Simplifying 1 + -30x + 18x2 = 0 Solving 1 + -30x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.05555555556 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '-0.05555555556' to each side of the equation. 0.05555555556 + -1.666666667x + -0.05555555556 + x2 = 0 + -0.05555555556 Reorder the terms: 0.05555555556 + -0.05555555556 + -1.666666667x + x2 = 0 + -0.05555555556 Combine like terms: 0.05555555556 + -0.05555555556 = 0.00000000000 0.00000000000 + -1.666666667x + x2 = 0 + -0.05555555556 -1.666666667x + x2 = 0 + -0.05555555556 Combine like terms: 0 + -0.05555555556 = -0.05555555556 -1.666666667x + x2 = -0.05555555556 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 = -0.05555555556 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = -0.05555555556 + 0.6944444447 Combine like terms: -0.05555555556 + 0.6944444447 = 0.63888888914 0.6944444447 + -1.666666667x + x2 = 0.63888888914 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 0.63888888914 Calculate the square root of the right side: 0.799305254 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 0.799305254 and -0.799305254.Subproblem 1
x + -0.8333333335 = 0.799305254 Simplifying x + -0.8333333335 = 0.799305254 Reorder the terms: -0.8333333335 + x = 0.799305254 Solving -0.8333333335 + x = 0.799305254 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 = 0.799305254 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 0.799305254 + 0.8333333335 x = 0.799305254 + 0.8333333335 Combine like terms: 0.799305254 + 0.8333333335 = 1.6326385875 x = 1.6326385875 Simplifying x = 1.6326385875Subproblem 2
x + -0.8333333335 = -0.799305254 Simplifying x + -0.8333333335 = -0.799305254 Reorder the terms: -0.8333333335 + x = -0.799305254 Solving -0.8333333335 + x = -0.799305254 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 = -0.799305254 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -0.799305254 + 0.8333333335 x = -0.799305254 + 0.8333333335 Combine like terms: -0.799305254 + 0.8333333335 = 0.0340280795 x = 0.0340280795 Simplifying x = 0.0340280795Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6326385875, 0.0340280795}Solution
x = {1.6326385875, 0.0340280795}
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