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Simplifying 12480X2 + -1300000X + -1927800 = 0 Reorder the terms: -1927800 + -1300000X + 12480X2 = 0 Solving -1927800 + -1300000X + 12480X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '40'. 40(-48195 + -32500X + 312X2) = 0 Ignore the factor 40.Subproblem 1
Set the factor '(-48195 + -32500X + 312X2)' equal to zero and attempt to solve: Simplifying -48195 + -32500X + 312X2 = 0 Solving -48195 + -32500X + 312X2 = 0 Begin completing the square. Divide all terms by 312 the coefficient of the squared term: Divide each side by '312'. -154.4711538 + -104.1666667X + X2 = 0 Move the constant term to the right: Add '154.4711538' to each side of the equation. -154.4711538 + -104.1666667X + 154.4711538 + X2 = 0 + 154.4711538 Reorder the terms: -154.4711538 + 154.4711538 + -104.1666667X + X2 = 0 + 154.4711538 Combine like terms: -154.4711538 + 154.4711538 = 0.0000000 0.0000000 + -104.1666667X + X2 = 0 + 154.4711538 -104.1666667X + X2 = 0 + 154.4711538 Combine like terms: 0 + 154.4711538 = 154.4711538 -104.1666667X + X2 = 154.4711538 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 = 154.4711538 + 2712.673613 Reorder the terms: 2712.673613 + -104.1666667X + X2 = 154.4711538 + 2712.673613 Combine like terms: 154.4711538 + 2712.673613 = 2867.1447668 2712.673613 + -104.1666667X + X2 = 2867.1447668 Factor a perfect square on the left side: (X + -52.08333335)(X + -52.08333335) = 2867.1447668 Calculate the square root of the right side: 53.545725943 Break this problem into two subproblems by setting (X + -52.08333335) equal to 53.545725943 and -53.545725943.Subproblem 1
X + -52.08333335 = 53.545725943 Simplifying X + -52.08333335 = 53.545725943 Reorder the terms: -52.08333335 + X = 53.545725943 Solving -52.08333335 + X = 53.545725943 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 = 53.545725943 + 52.08333335 Combine like terms: -52.08333335 + 52.08333335 = 0.00000000 0.00000000 + X = 53.545725943 + 52.08333335 X = 53.545725943 + 52.08333335 Combine like terms: 53.545725943 + 52.08333335 = 105.629059293 X = 105.629059293 Simplifying X = 105.629059293Subproblem 2
X + -52.08333335 = -53.545725943 Simplifying X + -52.08333335 = -53.545725943 Reorder the terms: -52.08333335 + X = -53.545725943 Solving -52.08333335 + X = -53.545725943 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 = -53.545725943 + 52.08333335 Combine like terms: -52.08333335 + 52.08333335 = 0.00000000 0.00000000 + X = -53.545725943 + 52.08333335 X = -53.545725943 + 52.08333335 Combine like terms: -53.545725943 + 52.08333335 = -1.462392593 X = -1.462392593 Simplifying X = -1.462392593Solution
The solution to the problem is based on the solutions from the subproblems. X = {105.629059293, -1.462392593}Solution
X = {105.629059293, -1.462392593}
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