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Simplifying 6x2 + -100x + 122 = 0 Reorder the terms: 122 + -100x + 6x2 = 0 Solving 122 + -100x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(61 + -50x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(61 + -50x + 3x2)' equal to zero and attempt to solve: Simplifying 61 + -50x + 3x2 = 0 Solving 61 + -50x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 20.33333333 + -16.66666667x + x2 = 0 Move the constant term to the right: Add '-20.33333333' to each side of the equation. 20.33333333 + -16.66666667x + -20.33333333 + x2 = 0 + -20.33333333 Reorder the terms: 20.33333333 + -20.33333333 + -16.66666667x + x2 = 0 + -20.33333333 Combine like terms: 20.33333333 + -20.33333333 = 0.00000000 0.00000000 + -16.66666667x + x2 = 0 + -20.33333333 -16.66666667x + x2 = 0 + -20.33333333 Combine like terms: 0 + -20.33333333 = -20.33333333 -16.66666667x + x2 = -20.33333333 The x term is -16.66666667x. Take half its coefficient (-8.333333335). Square it (69.44444447) and add it to both sides. Add '69.44444447' to each side of the equation. -16.66666667x + 69.44444447 + x2 = -20.33333333 + 69.44444447 Reorder the terms: 69.44444447 + -16.66666667x + x2 = -20.33333333 + 69.44444447 Combine like terms: -20.33333333 + 69.44444447 = 49.11111114 69.44444447 + -16.66666667x + x2 = 49.11111114 Factor a perfect square on the left side: (x + -8.333333335)(x + -8.333333335) = 49.11111114 Calculate the square root of the right side: 7.007932016 Break this problem into two subproblems by setting (x + -8.333333335) equal to 7.007932016 and -7.007932016.Subproblem 1
x + -8.333333335 = 7.007932016 Simplifying x + -8.333333335 = 7.007932016 Reorder the terms: -8.333333335 + x = 7.007932016 Solving -8.333333335 + x = 7.007932016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.333333335' to each side of the equation. -8.333333335 + 8.333333335 + x = 7.007932016 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = 7.007932016 + 8.333333335 x = 7.007932016 + 8.333333335 Combine like terms: 7.007932016 + 8.333333335 = 15.341265351 x = 15.341265351 Simplifying x = 15.341265351Subproblem 2
x + -8.333333335 = -7.007932016 Simplifying x + -8.333333335 = -7.007932016 Reorder the terms: -8.333333335 + x = -7.007932016 Solving -8.333333335 + x = -7.007932016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.333333335' to each side of the equation. -8.333333335 + 8.333333335 + x = -7.007932016 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = -7.007932016 + 8.333333335 x = -7.007932016 + 8.333333335 Combine like terms: -7.007932016 + 8.333333335 = 1.325401319 x = 1.325401319 Simplifying x = 1.325401319Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.341265351, 1.325401319}Solution
x = {15.341265351, 1.325401319}
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