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Simplifying -2x2 + 156x + -2720 = 0 Reorder the terms: -2720 + 156x + -2x2 = 0 Solving -2720 + 156x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1360 + 78x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1360 + 78x + -1x2)' equal to zero and attempt to solve: Simplifying -1360 + 78x + -1x2 = 0 Solving -1360 + 78x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1360 + -78x + x2 = 0 Move the constant term to the right: Add '-1360' to each side of the equation. 1360 + -78x + -1360 + x2 = 0 + -1360 Reorder the terms: 1360 + -1360 + -78x + x2 = 0 + -1360 Combine like terms: 1360 + -1360 = 0 0 + -78x + x2 = 0 + -1360 -78x + x2 = 0 + -1360 Combine like terms: 0 + -1360 = -1360 -78x + x2 = -1360 The x term is -78x. Take half its coefficient (-39). Square it (1521) and add it to both sides. Add '1521' to each side of the equation. -78x + 1521 + x2 = -1360 + 1521 Reorder the terms: 1521 + -78x + x2 = -1360 + 1521 Combine like terms: -1360 + 1521 = 161 1521 + -78x + x2 = 161 Factor a perfect square on the left side: (x + -39)(x + -39) = 161 Calculate the square root of the right side: 12.68857754 Break this problem into two subproblems by setting (x + -39) equal to 12.68857754 and -12.68857754.Subproblem 1
x + -39 = 12.68857754 Simplifying x + -39 = 12.68857754 Reorder the terms: -39 + x = 12.68857754 Solving -39 + x = 12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '39' to each side of the equation. -39 + 39 + x = 12.68857754 + 39 Combine like terms: -39 + 39 = 0 0 + x = 12.68857754 + 39 x = 12.68857754 + 39 Combine like terms: 12.68857754 + 39 = 51.68857754 x = 51.68857754 Simplifying x = 51.68857754Subproblem 2
x + -39 = -12.68857754 Simplifying x + -39 = -12.68857754 Reorder the terms: -39 + x = -12.68857754 Solving -39 + x = -12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '39' to each side of the equation. -39 + 39 + x = -12.68857754 + 39 Combine like terms: -39 + 39 = 0 0 + x = -12.68857754 + 39 x = -12.68857754 + 39 Combine like terms: -12.68857754 + 39 = 26.31142246 x = 26.31142246 Simplifying x = 26.31142246Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.68857754, 26.31142246}Solution
x = {51.68857754, 26.31142246}
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