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Simplifying 144x2 + -120x = 4 Reorder the terms: -120x + 144x2 = 4 Solving -120x + 144x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + -120x + 144x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -120x + 144x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + -30x + 36x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -30x + 36x2)' equal to zero and attempt to solve: Simplifying -1 + -30x + 36x2 = 0 Solving -1 + -30x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.02777777778 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '0.02777777778' to each side of the equation. -0.02777777778 + -0.8333333333x + 0.02777777778 + x2 = 0 + 0.02777777778 Reorder the terms: -0.02777777778 + 0.02777777778 + -0.8333333333x + x2 = 0 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + -0.8333333333x + x2 = 0 + 0.02777777778 -0.8333333333x + x2 = 0 + 0.02777777778 Combine like terms: 0 + 0.02777777778 = 0.02777777778 -0.8333333333x + x2 = 0.02777777778 The x term is -0.8333333333x. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x + 0.1736111111 + x2 = 0.02777777778 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = 0.02777777778 + 0.1736111111 Combine like terms: 0.02777777778 + 0.1736111111 = 0.20138888888 0.1736111111 + -0.8333333333x + x2 = 0.20138888888 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = 0.20138888888 Calculate the square root of the right side: 0.448763734 Break this problem into two subproblems by setting (x + -0.4166666667) equal to 0.448763734 and -0.448763734.Subproblem 1
x + -0.4166666667 = 0.448763734 Simplifying x + -0.4166666667 = 0.448763734 Reorder the terms: -0.4166666667 + x = 0.448763734 Solving -0.4166666667 + x = 0.448763734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = 0.448763734 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = 0.448763734 + 0.4166666667 x = 0.448763734 + 0.4166666667 Combine like terms: 0.448763734 + 0.4166666667 = 0.8654304007 x = 0.8654304007 Simplifying x = 0.8654304007Subproblem 2
x + -0.4166666667 = -0.448763734 Simplifying x + -0.4166666667 = -0.448763734 Reorder the terms: -0.4166666667 + x = -0.448763734 Solving -0.4166666667 + x = -0.448763734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = -0.448763734 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = -0.448763734 + 0.4166666667 x = -0.448763734 + 0.4166666667 Combine like terms: -0.448763734 + 0.4166666667 = -0.0320970673 x = -0.0320970673 Simplifying x = -0.0320970673Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8654304007, -0.0320970673}Solution
x = {0.8654304007, -0.0320970673}
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