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Simplifying -36x2 + 6000x + 10 = 0 Reorder the terms: 10 + 6000x + -36x2 = 0 Solving 10 + 6000x + -36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 3000x + -18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 3000x + -18x2)' equal to zero and attempt to solve: Simplifying 5 + 3000x + -18x2 = 0 Solving 5 + 3000x + -18x2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. -0.2777777778 + -166.6666667x + x2 = 0 Move the constant term to the right: Add '0.2777777778' to each side of the equation. -0.2777777778 + -166.6666667x + 0.2777777778 + x2 = 0 + 0.2777777778 Reorder the terms: -0.2777777778 + 0.2777777778 + -166.6666667x + x2 = 0 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + -166.6666667x + x2 = 0 + 0.2777777778 -166.6666667x + x2 = 0 + 0.2777777778 Combine like terms: 0 + 0.2777777778 = 0.2777777778 -166.6666667x + x2 = 0.2777777778 The x term is -166.6666667x. Take half its coefficient (-83.33333335). Square it (6944.444447) and add it to both sides. Add '6944.444447' to each side of the equation. -166.6666667x + 6944.444447 + x2 = 0.2777777778 + 6944.444447 Reorder the terms: 6944.444447 + -166.6666667x + x2 = 0.2777777778 + 6944.444447 Combine like terms: 0.2777777778 + 6944.444447 = 6944.7222247778 6944.444447 + -166.6666667x + x2 = 6944.7222247778 Factor a perfect square on the left side: (x + -83.33333335)(x + -83.33333335) = 6944.7222247778 Calculate the square root of the right side: 83.334999999 Break this problem into two subproblems by setting (x + -83.33333335) equal to 83.334999999 and -83.334999999.Subproblem 1
x + -83.33333335 = 83.334999999 Simplifying x + -83.33333335 = 83.334999999 Reorder the terms: -83.33333335 + x = 83.334999999 Solving -83.33333335 + x = 83.334999999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '83.33333335' to each side of the equation. -83.33333335 + 83.33333335 + x = 83.334999999 + 83.33333335 Combine like terms: -83.33333335 + 83.33333335 = 0.00000000 0.00000000 + x = 83.334999999 + 83.33333335 x = 83.334999999 + 83.33333335 Combine like terms: 83.334999999 + 83.33333335 = 166.668333349 x = 166.668333349 Simplifying x = 166.668333349Subproblem 2
x + -83.33333335 = -83.334999999 Simplifying x + -83.33333335 = -83.334999999 Reorder the terms: -83.33333335 + x = -83.334999999 Solving -83.33333335 + x = -83.334999999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '83.33333335' to each side of the equation. -83.33333335 + 83.33333335 + x = -83.334999999 + 83.33333335 Combine like terms: -83.33333335 + 83.33333335 = 0.00000000 0.00000000 + x = -83.334999999 + 83.33333335 x = -83.334999999 + 83.33333335 Combine like terms: -83.334999999 + 83.33333335 = -0.001666649 x = -0.001666649 Simplifying x = -0.001666649Solution
The solution to the problem is based on the solutions from the subproblems. x = {166.668333349, -0.001666649}Solution
x = {166.668333349, -0.001666649}
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