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Simplifying 0 = 6x2 + -100x + 4 Reorder the terms: 0 = 4 + -100x + 6x2 Solving 0 = 4 + -100x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + 100x + -6x2 = 4 + -100x + 6x2 + -4 + 100x + -6x2 Reorder the terms: -4 + 100x + -6x2 = 4 + -4 + -100x + 100x + 6x2 + -6x2 Combine like terms: 4 + -4 = 0 -4 + 100x + -6x2 = 0 + -100x + 100x + 6x2 + -6x2 -4 + 100x + -6x2 = -100x + 100x + 6x2 + -6x2 Combine like terms: -100x + 100x = 0 -4 + 100x + -6x2 = 0 + 6x2 + -6x2 -4 + 100x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -4 + 100x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 50x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 50x + -3x2)' equal to zero and attempt to solve: Simplifying -2 + 50x + -3x2 = 0 Solving -2 + 50x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 0.6666666667 + -16.66666667x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -16.66666667x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -16.66666667x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -16.66666667x + x2 = 0 + -0.6666666667 -16.66666667x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -16.66666667x + x2 = -0.6666666667 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 = -0.6666666667 + 69.44444447 Reorder the terms: 69.44444447 + -16.66666667x + x2 = -0.6666666667 + 69.44444447 Combine like terms: -0.6666666667 + 69.44444447 = 68.7777778033 69.44444447 + -16.66666667x + x2 = 68.7777778033 Factor a perfect square on the left side: (x + -8.333333335)(x + -8.333333335) = 68.7777778033 Calculate the square root of the right side: 8.293236871 Break this problem into two subproblems by setting (x + -8.333333335) equal to 8.293236871 and -8.293236871.Subproblem 1
x + -8.333333335 = 8.293236871 Simplifying x + -8.333333335 = 8.293236871 Reorder the terms: -8.333333335 + x = 8.293236871 Solving -8.333333335 + x = 8.293236871 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 = 8.293236871 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = 8.293236871 + 8.333333335 x = 8.293236871 + 8.333333335 Combine like terms: 8.293236871 + 8.333333335 = 16.626570206 x = 16.626570206 Simplifying x = 16.626570206Subproblem 2
x + -8.333333335 = -8.293236871 Simplifying x + -8.333333335 = -8.293236871 Reorder the terms: -8.333333335 + x = -8.293236871 Solving -8.333333335 + x = -8.293236871 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 = -8.293236871 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = -8.293236871 + 8.333333335 x = -8.293236871 + 8.333333335 Combine like terms: -8.293236871 + 8.333333335 = 0.040096464 x = 0.040096464 Simplifying x = 0.040096464Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.626570206, 0.040096464}Solution
x = {16.626570206, 0.040096464}
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