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Simplifying 120x2 + -272x + 102 = 0 Reorder the terms: 102 + -272x + 120x2 = 0 Solving 102 + -272x + 120x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(51 + -136x + 60x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(51 + -136x + 60x2)' equal to zero and attempt to solve: Simplifying 51 + -136x + 60x2 = 0 Solving 51 + -136x + 60x2 = 0 Begin completing the square. Divide all terms by 60 the coefficient of the squared term: Divide each side by '60'. 0.85 + -2.266666667x + x2 = 0.0 Move the constant term to the right: Add '-0.85' to each side of the equation. 0.85 + -2.266666667x + -0.85 + x2 = 0.0 + -0.85 Reorder the terms: 0.85 + -0.85 + -2.266666667x + x2 = 0.0 + -0.85 Combine like terms: 0.85 + -0.85 = 0.00 0.00 + -2.266666667x + x2 = 0.0 + -0.85 -2.266666667x + x2 = 0.0 + -0.85 Combine like terms: 0.0 + -0.85 = -0.85 -2.266666667x + x2 = -0.85 The x term is -2.266666667x. Take half its coefficient (-1.133333334). Square it (1.284444446) and add it to both sides. Add '1.284444446' to each side of the equation. -2.266666667x + 1.284444446 + x2 = -0.85 + 1.284444446 Reorder the terms: 1.284444446 + -2.266666667x + x2 = -0.85 + 1.284444446 Combine like terms: -0.85 + 1.284444446 = 0.434444446 1.284444446 + -2.266666667x + x2 = 0.434444446 Factor a perfect square on the left side: (x + -1.133333334)(x + -1.133333334) = 0.434444446 Calculate the square root of the right side: 0.659123999 Break this problem into two subproblems by setting (x + -1.133333334) equal to 0.659123999 and -0.659123999.Subproblem 1
x + -1.133333334 = 0.659123999 Simplifying x + -1.133333334 = 0.659123999 Reorder the terms: -1.133333334 + x = 0.659123999 Solving -1.133333334 + x = 0.659123999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.133333334' to each side of the equation. -1.133333334 + 1.133333334 + x = 0.659123999 + 1.133333334 Combine like terms: -1.133333334 + 1.133333334 = 0.000000000 0.000000000 + x = 0.659123999 + 1.133333334 x = 0.659123999 + 1.133333334 Combine like terms: 0.659123999 + 1.133333334 = 1.792457333 x = 1.792457333 Simplifying x = 1.792457333Subproblem 2
x + -1.133333334 = -0.659123999 Simplifying x + -1.133333334 = -0.659123999 Reorder the terms: -1.133333334 + x = -0.659123999 Solving -1.133333334 + x = -0.659123999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.133333334' to each side of the equation. -1.133333334 + 1.133333334 + x = -0.659123999 + 1.133333334 Combine like terms: -1.133333334 + 1.133333334 = 0.000000000 0.000000000 + x = -0.659123999 + 1.133333334 x = -0.659123999 + 1.133333334 Combine like terms: -0.659123999 + 1.133333334 = 0.474209335 x = 0.474209335 Simplifying x = 0.474209335Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.792457333, 0.474209335}Solution
x = {1.792457333, 0.474209335}
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