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Simplifying 12480X2 + -1300000X + -19278000 = 0 Reorder the terms: -19278000 + -1300000X + 12480X2 = 0 Solving -19278000 + -1300000X + 12480X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '80'. 80(-240975 + -16250X + 156X2) = 0 Ignore the factor 80.Subproblem 1
Set the factor '(-240975 + -16250X + 156X2)' equal to zero and attempt to solve: Simplifying -240975 + -16250X + 156X2 = 0 Solving -240975 + -16250X + 156X2 = 0 Begin completing the square. Divide all terms by 156 the coefficient of the squared term: Divide each side by '156'. -1544.711538 + -104.1666667X + X2 = 0 Move the constant term to the right: Add '1544.711538' to each side of the equation. -1544.711538 + -104.1666667X + 1544.711538 + X2 = 0 + 1544.711538 Reorder the terms: -1544.711538 + 1544.711538 + -104.1666667X + X2 = 0 + 1544.711538 Combine like terms: -1544.711538 + 1544.711538 = 0.000000 0.000000 + -104.1666667X + X2 = 0 + 1544.711538 -104.1666667X + X2 = 0 + 1544.711538 Combine like terms: 0 + 1544.711538 = 1544.711538 -104.1666667X + X2 = 1544.711538 The X term is -104.1666667X. Take half its coefficient (-52.08333335). Square it (2712.673613) and add it to both sides. Add '2712.673613' to each side of the equation. -104.1666667X + 2712.673613 + X2 = 1544.711538 + 2712.673613 Reorder the terms: 2712.673613 + -104.1666667X + X2 = 1544.711538 + 2712.673613 Combine like terms: 1544.711538 + 2712.673613 = 4257.385151 2712.673613 + -104.1666667X + X2 = 4257.385151 Factor a perfect square on the left side: (X + -52.08333335)(X + -52.08333335) = 4257.385151 Calculate the square root of the right side: 65.24864099 Break this problem into two subproblems by setting (X + -52.08333335) equal to 65.24864099 and -65.24864099.Subproblem 1
X + -52.08333335 = 65.24864099 Simplifying X + -52.08333335 = 65.24864099 Reorder the terms: -52.08333335 + X = 65.24864099 Solving -52.08333335 + X = 65.24864099 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '52.08333335' to each side of the equation. -52.08333335 + 52.08333335 + X = 65.24864099 + 52.08333335 Combine like terms: -52.08333335 + 52.08333335 = 0.00000000 0.00000000 + X = 65.24864099 + 52.08333335 X = 65.24864099 + 52.08333335 Combine like terms: 65.24864099 + 52.08333335 = 117.33197434 X = 117.33197434 Simplifying X = 117.33197434Subproblem 2
X + -52.08333335 = -65.24864099 Simplifying X + -52.08333335 = -65.24864099 Reorder the terms: -52.08333335 + X = -65.24864099 Solving -52.08333335 + X = -65.24864099 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '52.08333335' to each side of the equation. -52.08333335 + 52.08333335 + X = -65.24864099 + 52.08333335 Combine like terms: -52.08333335 + 52.08333335 = 0.00000000 0.00000000 + X = -65.24864099 + 52.08333335 X = -65.24864099 + 52.08333335 Combine like terms: -65.24864099 + 52.08333335 = -13.16530764 X = -13.16530764 Simplifying X = -13.16530764Solution
The solution to the problem is based on the solutions from the subproblems. X = {117.33197434, -13.16530764}Solution
X = {117.33197434, -13.16530764}
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