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Simplifying x2 + 74x + -120 = 0 Reorder the terms: -120 + 74x + x2 = 0 Solving -120 + 74x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + 74x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 74x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 74x + x2 = 0 + 120 74x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 74x + x2 = 120 The x term is 74x. Take half its coefficient (37). Square it (1369) and add it to both sides. Add '1369' to each side of the equation. 74x + 1369 + x2 = 120 + 1369 Reorder the terms: 1369 + 74x + x2 = 120 + 1369 Combine like terms: 120 + 1369 = 1489 1369 + 74x + x2 = 1489 Factor a perfect square on the left side: (x + 37)(x + 37) = 1489 Calculate the square root of the right side: 38.587562763 Break this problem into two subproblems by setting (x + 37) equal to 38.587562763 and -38.587562763.Subproblem 1
x + 37 = 38.587562763 Simplifying x + 37 = 38.587562763 Reorder the terms: 37 + x = 38.587562763 Solving 37 + x = 38.587562763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -37 + x = 38.587562763 + -37 Combine like terms: 37 + -37 = 0 0 + x = 38.587562763 + -37 x = 38.587562763 + -37 Combine like terms: 38.587562763 + -37 = 1.587562763 x = 1.587562763 Simplifying x = 1.587562763Subproblem 2
x + 37 = -38.587562763 Simplifying x + 37 = -38.587562763 Reorder the terms: 37 + x = -38.587562763 Solving 37 + x = -38.587562763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -37 + x = -38.587562763 + -37 Combine like terms: 37 + -37 = 0 0 + x = -38.587562763 + -37 x = -38.587562763 + -37 Combine like terms: -38.587562763 + -37 = -75.587562763 x = -75.587562763 Simplifying x = -75.587562763Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.587562763, -75.587562763}
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