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Simplifying 0 = 6x2 + -100x + 38 Reorder the terms: 0 = 38 + -100x + 6x2 Solving 0 = 38 + -100x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -38 = -38 -38 + 100x + -6x2 = 38 + -100x + 6x2 + -38 + 100x + -6x2 Reorder the terms: -38 + 100x + -6x2 = 38 + -38 + -100x + 100x + 6x2 + -6x2 Combine like terms: 38 + -38 = 0 -38 + 100x + -6x2 = 0 + -100x + 100x + 6x2 + -6x2 -38 + 100x + -6x2 = -100x + 100x + 6x2 + -6x2 Combine like terms: -100x + 100x = 0 -38 + 100x + -6x2 = 0 + 6x2 + -6x2 -38 + 100x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -38 + 100x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-19 + 50x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + 50x + -3x2)' equal to zero and attempt to solve: Simplifying -19 + 50x + -3x2 = 0 Solving -19 + 50x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 6.333333333 + -16.66666667x + x2 = 0 Move the constant term to the right: Add '-6.333333333' to each side of the equation. 6.333333333 + -16.66666667x + -6.333333333 + x2 = 0 + -6.333333333 Reorder the terms: 6.333333333 + -6.333333333 + -16.66666667x + x2 = 0 + -6.333333333 Combine like terms: 6.333333333 + -6.333333333 = 0.000000000 0.000000000 + -16.66666667x + x2 = 0 + -6.333333333 -16.66666667x + x2 = 0 + -6.333333333 Combine like terms: 0 + -6.333333333 = -6.333333333 -16.66666667x + x2 = -6.333333333 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 = -6.333333333 + 69.44444447 Reorder the terms: 69.44444447 + -16.66666667x + x2 = -6.333333333 + 69.44444447 Combine like terms: -6.333333333 + 69.44444447 = 63.111111137 69.44444447 + -16.66666667x + x2 = 63.111111137 Factor a perfect square on the left side: (x + -8.333333335)(x + -8.333333335) = 63.111111137 Calculate the square root of the right side: 7.944250194 Break this problem into two subproblems by setting (x + -8.333333335) equal to 7.944250194 and -7.944250194.Subproblem 1
x + -8.333333335 = 7.944250194 Simplifying x + -8.333333335 = 7.944250194 Reorder the terms: -8.333333335 + x = 7.944250194 Solving -8.333333335 + x = 7.944250194 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 = 7.944250194 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = 7.944250194 + 8.333333335 x = 7.944250194 + 8.333333335 Combine like terms: 7.944250194 + 8.333333335 = 16.277583529 x = 16.277583529 Simplifying x = 16.277583529Subproblem 2
x + -8.333333335 = -7.944250194 Simplifying x + -8.333333335 = -7.944250194 Reorder the terms: -8.333333335 + x = -7.944250194 Solving -8.333333335 + x = -7.944250194 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 = -7.944250194 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = -7.944250194 + 8.333333335 x = -7.944250194 + 8.333333335 Combine like terms: -7.944250194 + 8.333333335 = 0.389083141 x = 0.389083141 Simplifying x = 0.389083141Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.277583529, 0.389083141}Solution
x = {16.277583529, 0.389083141}
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