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Simplifying 144x2 + 48x + 2 = 0 Reorder the terms: 2 + 48x + 144x2 = 0 Solving 2 + 48x + 144x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 24x + 72x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 24x + 72x2)' equal to zero and attempt to solve: Simplifying 1 + 24x + 72x2 = 0 Solving 1 + 24x + 72x2 = 0 Begin completing the square. Divide all terms by 72 the coefficient of the squared term: Divide each side by '72'. 0.01388888889 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.01388888889' to each side of the equation. 0.01388888889 + 0.3333333333x + -0.01388888889 + x2 = 0 + -0.01388888889 Reorder the terms: 0.01388888889 + -0.01388888889 + 0.3333333333x + x2 = 0 + -0.01388888889 Combine like terms: 0.01388888889 + -0.01388888889 = 0.00000000000 0.00000000000 + 0.3333333333x + x2 = 0 + -0.01388888889 0.3333333333x + x2 = 0 + -0.01388888889 Combine like terms: 0 + -0.01388888889 = -0.01388888889 0.3333333333x + x2 = -0.01388888889 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 = -0.01388888889 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = -0.01388888889 + 0.02777777779 Combine like terms: -0.01388888889 + 0.02777777779 = 0.0138888889 0.02777777779 + 0.3333333333x + x2 = 0.0138888889 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 0.0138888889 Calculate the square root of the right side: 0.11785113 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 0.11785113 and -0.11785113.Subproblem 1
x + 0.1666666667 = 0.11785113 Simplifying x + 0.1666666667 = 0.11785113 Reorder the terms: 0.1666666667 + x = 0.11785113 Solving 0.1666666667 + x = 0.11785113 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 = 0.11785113 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.11785113 + -0.1666666667 x = 0.11785113 + -0.1666666667 Combine like terms: 0.11785113 + -0.1666666667 = -0.0488155367 x = -0.0488155367 Simplifying x = -0.0488155367Subproblem 2
x + 0.1666666667 = -0.11785113 Simplifying x + 0.1666666667 = -0.11785113 Reorder the terms: 0.1666666667 + x = -0.11785113 Solving 0.1666666667 + x = -0.11785113 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 = -0.11785113 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.11785113 + -0.1666666667 x = -0.11785113 + -0.1666666667 Combine like terms: -0.11785113 + -0.1666666667 = -0.2845177967 x = -0.2845177967 Simplifying x = -0.2845177967Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0488155367, -0.2845177967}Solution
x = {-0.0488155367, -0.2845177967}
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