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Simplifying x2 + 124x + -770 = 0 Reorder the terms: -770 + 124x + x2 = 0 Solving -770 + 124x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '770' to each side of the equation. -770 + 124x + 770 + x2 = 0 + 770 Reorder the terms: -770 + 770 + 124x + x2 = 0 + 770 Combine like terms: -770 + 770 = 0 0 + 124x + x2 = 0 + 770 124x + x2 = 0 + 770 Combine like terms: 0 + 770 = 770 124x + x2 = 770 The x term is 124x. Take half its coefficient (62). Square it (3844) and add it to both sides. Add '3844' to each side of the equation. 124x + 3844 + x2 = 770 + 3844 Reorder the terms: 3844 + 124x + x2 = 770 + 3844 Combine like terms: 770 + 3844 = 4614 3844 + 124x + x2 = 4614 Factor a perfect square on the left side: (x + 62)(x + 62) = 4614 Calculate the square root of the right side: 67.926430791 Break this problem into two subproblems by setting (x + 62) equal to 67.926430791 and -67.926430791.Subproblem 1
x + 62 = 67.926430791 Simplifying x + 62 = 67.926430791 Reorder the terms: 62 + x = 67.926430791 Solving 62 + x = 67.926430791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-62' to each side of the equation. 62 + -62 + x = 67.926430791 + -62 Combine like terms: 62 + -62 = 0 0 + x = 67.926430791 + -62 x = 67.926430791 + -62 Combine like terms: 67.926430791 + -62 = 5.926430791 x = 5.926430791 Simplifying x = 5.926430791Subproblem 2
x + 62 = -67.926430791 Simplifying x + 62 = -67.926430791 Reorder the terms: 62 + x = -67.926430791 Solving 62 + x = -67.926430791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-62' to each side of the equation. 62 + -62 + x = -67.926430791 + -62 Combine like terms: 62 + -62 = 0 0 + x = -67.926430791 + -62 x = -67.926430791 + -62 Combine like terms: -67.926430791 + -62 = -129.926430791 x = -129.926430791 Simplifying x = -129.926430791Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.926430791, -129.926430791}
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