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Simplifying 225x2 + 60x + 2 = 0 Reorder the terms: 2 + 60x + 225x2 = 0 Solving 2 + 60x + 225x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 225 the coefficient of the squared term: Divide each side by '225'. 0.008888888889 + 0.2666666667x + x2 = 0 Move the constant term to the right: Add '-0.008888888889' to each side of the equation. 0.008888888889 + 0.2666666667x + -0.008888888889 + x2 = 0 + -0.008888888889 Reorder the terms: 0.008888888889 + -0.008888888889 + 0.2666666667x + x2 = 0 + -0.008888888889 Combine like terms: 0.008888888889 + -0.008888888889 = 0.000000000000 0.000000000000 + 0.2666666667x + x2 = 0 + -0.008888888889 0.2666666667x + x2 = 0 + -0.008888888889 Combine like terms: 0 + -0.008888888889 = -0.008888888889 0.2666666667x + x2 = -0.008888888889 The x term is 0.2666666667x. Take half its coefficient (0.1333333334). Square it (0.01777777780) and add it to both sides. Add '0.01777777780' to each side of the equation. 0.2666666667x + 0.01777777780 + x2 = -0.008888888889 + 0.01777777780 Reorder the terms: 0.01777777780 + 0.2666666667x + x2 = -0.008888888889 + 0.01777777780 Combine like terms: -0.008888888889 + 0.01777777780 = 0.008888888911 0.01777777780 + 0.2666666667x + x2 = 0.008888888911 Factor a perfect square on the left side: (x + 0.1333333334)(x + 0.1333333334) = 0.008888888911 Calculate the square root of the right side: 0.094280904 Break this problem into two subproblems by setting (x + 0.1333333334) equal to 0.094280904 and -0.094280904.Subproblem 1
x + 0.1333333334 = 0.094280904 Simplifying x + 0.1333333334 = 0.094280904 Reorder the terms: 0.1333333334 + x = 0.094280904 Solving 0.1333333334 + x = 0.094280904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1333333334' to each side of the equation. 0.1333333334 + -0.1333333334 + x = 0.094280904 + -0.1333333334 Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000 0.0000000000 + x = 0.094280904 + -0.1333333334 x = 0.094280904 + -0.1333333334 Combine like terms: 0.094280904 + -0.1333333334 = -0.0390524294 x = -0.0390524294 Simplifying x = -0.0390524294Subproblem 2
x + 0.1333333334 = -0.094280904 Simplifying x + 0.1333333334 = -0.094280904 Reorder the terms: 0.1333333334 + x = -0.094280904 Solving 0.1333333334 + x = -0.094280904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1333333334' to each side of the equation. 0.1333333334 + -0.1333333334 + x = -0.094280904 + -0.1333333334 Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000 0.0000000000 + x = -0.094280904 + -0.1333333334 x = -0.094280904 + -0.1333333334 Combine like terms: -0.094280904 + -0.1333333334 = -0.2276142374 x = -0.2276142374 Simplifying x = -0.2276142374Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0390524294, -0.2276142374}
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