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Simplifying 36x2 + -60x + 3 = 0 Reorder the terms: 3 + -60x + 36x2 = 0 Solving 3 + -60x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -20x + 12x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -20x + 12x2)' equal to zero and attempt to solve: Simplifying 1 + -20x + 12x2 = 0 Solving 1 + -20x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.08333333333 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '-0.08333333333' to each side of the equation. 0.08333333333 + -1.666666667x + -0.08333333333 + x2 = 0 + -0.08333333333 Reorder the terms: 0.08333333333 + -0.08333333333 + -1.666666667x + x2 = 0 + -0.08333333333 Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000 0.00000000000 + -1.666666667x + x2 = 0 + -0.08333333333 -1.666666667x + x2 = 0 + -0.08333333333 Combine like terms: 0 + -0.08333333333 = -0.08333333333 -1.666666667x + x2 = -0.08333333333 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 = -0.08333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = -0.08333333333 + 0.6944444447 Combine like terms: -0.08333333333 + 0.6944444447 = 0.61111111137 0.6944444447 + -1.666666667x + x2 = 0.61111111137 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 0.61111111137 Calculate the square root of the right side: 0.78173596 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 0.78173596 and -0.78173596.Subproblem 1
x + -0.8333333335 = 0.78173596 Simplifying x + -0.8333333335 = 0.78173596 Reorder the terms: -0.8333333335 + x = 0.78173596 Solving -0.8333333335 + x = 0.78173596 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 = 0.78173596 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 0.78173596 + 0.8333333335 x = 0.78173596 + 0.8333333335 Combine like terms: 0.78173596 + 0.8333333335 = 1.6150692935 x = 1.6150692935 Simplifying x = 1.6150692935Subproblem 2
x + -0.8333333335 = -0.78173596 Simplifying x + -0.8333333335 = -0.78173596 Reorder the terms: -0.8333333335 + x = -0.78173596 Solving -0.8333333335 + x = -0.78173596 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 = -0.78173596 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -0.78173596 + 0.8333333335 x = -0.78173596 + 0.8333333335 Combine like terms: -0.78173596 + 0.8333333335 = 0.0515973735 x = 0.0515973735 Simplifying x = 0.0515973735Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6150692935, 0.0515973735}Solution
x = {1.6150692935, 0.0515973735}
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