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Simplifying x2 + 118x + -378 = 0 Reorder the terms: -378 + 118x + x2 = 0 Solving -378 + 118x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '378' to each side of the equation. -378 + 118x + 378 + x2 = 0 + 378 Reorder the terms: -378 + 378 + 118x + x2 = 0 + 378 Combine like terms: -378 + 378 = 0 0 + 118x + x2 = 0 + 378 118x + x2 = 0 + 378 Combine like terms: 0 + 378 = 378 118x + x2 = 378 The x term is 118x. Take half its coefficient (59). Square it (3481) and add it to both sides. Add '3481' to each side of the equation. 118x + 3481 + x2 = 378 + 3481 Reorder the terms: 3481 + 118x + x2 = 378 + 3481 Combine like terms: 378 + 3481 = 3859 3481 + 118x + x2 = 3859 Factor a perfect square on the left side: (x + 59)(x + 59) = 3859 Calculate the square root of the right side: 62.120849962 Break this problem into two subproblems by setting (x + 59) equal to 62.120849962 and -62.120849962.Subproblem 1
x + 59 = 62.120849962 Simplifying x + 59 = 62.120849962 Reorder the terms: 59 + x = 62.120849962 Solving 59 + x = 62.120849962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-59' to each side of the equation. 59 + -59 + x = 62.120849962 + -59 Combine like terms: 59 + -59 = 0 0 + x = 62.120849962 + -59 x = 62.120849962 + -59 Combine like terms: 62.120849962 + -59 = 3.120849962 x = 3.120849962 Simplifying x = 3.120849962Subproblem 2
x + 59 = -62.120849962 Simplifying x + 59 = -62.120849962 Reorder the terms: 59 + x = -62.120849962 Solving 59 + x = -62.120849962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-59' to each side of the equation. 59 + -59 + x = -62.120849962 + -59 Combine like terms: 59 + -59 = 0 0 + x = -62.120849962 + -59 x = -62.120849962 + -59 Combine like terms: -62.120849962 + -59 = -121.120849962 x = -121.120849962 Simplifying x = -121.120849962Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.120849962, -121.120849962}
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