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Simplifying 6x2 + 100x = 73 Reorder the terms: 100x + 6x2 = 73 Solving 100x + 6x2 = 73 Solving for variable 'x'. Reorder the terms: -73 + 100x + 6x2 = 73 + -73 Combine like terms: 73 + -73 = 0 -73 + 100x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -12.16666667 + 16.66666667x + x2 = 0 Move the constant term to the right: Add '12.16666667' to each side of the equation. -12.16666667 + 16.66666667x + 12.16666667 + x2 = 0 + 12.16666667 Reorder the terms: -12.16666667 + 12.16666667 + 16.66666667x + x2 = 0 + 12.16666667 Combine like terms: -12.16666667 + 12.16666667 = 0.00000000 0.00000000 + 16.66666667x + x2 = 0 + 12.16666667 16.66666667x + x2 = 0 + 12.16666667 Combine like terms: 0 + 12.16666667 = 12.16666667 16.66666667x + x2 = 12.16666667 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 = 12.16666667 + 69.44444447 Reorder the terms: 69.44444447 + 16.66666667x + x2 = 12.16666667 + 69.44444447 Combine like terms: 12.16666667 + 69.44444447 = 81.61111114 69.44444447 + 16.66666667x + x2 = 81.61111114 Factor a perfect square on the left side: (x + 8.333333335)(x + 8.333333335) = 81.61111114 Calculate the square root of the right side: 9.033886824 Break this problem into two subproblems by setting (x + 8.333333335) equal to 9.033886824 and -9.033886824.Subproblem 1
x + 8.333333335 = 9.033886824 Simplifying x + 8.333333335 = 9.033886824 Reorder the terms: 8.333333335 + x = 9.033886824 Solving 8.333333335 + x = 9.033886824 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 = 9.033886824 + -8.333333335 Combine like terms: 8.333333335 + -8.333333335 = 0.000000000 0.000000000 + x = 9.033886824 + -8.333333335 x = 9.033886824 + -8.333333335 Combine like terms: 9.033886824 + -8.333333335 = 0.700553489 x = 0.700553489 Simplifying x = 0.700553489Subproblem 2
x + 8.333333335 = -9.033886824 Simplifying x + 8.333333335 = -9.033886824 Reorder the terms: 8.333333335 + x = -9.033886824 Solving 8.333333335 + x = -9.033886824 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 = -9.033886824 + -8.333333335 Combine like terms: 8.333333335 + -8.333333335 = 0.000000000 0.000000000 + x = -9.033886824 + -8.333333335 x = -9.033886824 + -8.333333335 Combine like terms: -9.033886824 + -8.333333335 = -17.367220159 x = -17.367220159 Simplifying x = -17.367220159Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.700553489, -17.367220159}
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