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Simplifying x2 + 124x + 49 = 1000 Reorder the terms: 49 + 124x + x2 = 1000 Solving 49 + 124x + x2 = 1000 Solving for variable 'x'. Reorder the terms: 49 + -1000 + 124x + x2 = 1000 + -1000 Combine like terms: 49 + -1000 = -951 -951 + 124x + x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -951 + 124x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '951' to each side of the equation. -951 + 124x + 951 + x2 = 0 + 951 Reorder the terms: -951 + 951 + 124x + x2 = 0 + 951 Combine like terms: -951 + 951 = 0 0 + 124x + x2 = 0 + 951 124x + x2 = 0 + 951 Combine like terms: 0 + 951 = 951 124x + x2 = 951 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 = 951 + 3844 Reorder the terms: 3844 + 124x + x2 = 951 + 3844 Combine like terms: 951 + 3844 = 4795 3844 + 124x + x2 = 4795 Factor a perfect square on the left side: (x + 62)(x + 62) = 4795 Calculate the square root of the right side: 69.245938509 Break this problem into two subproblems by setting (x + 62) equal to 69.245938509 and -69.245938509.Subproblem 1
x + 62 = 69.245938509 Simplifying x + 62 = 69.245938509 Reorder the terms: 62 + x = 69.245938509 Solving 62 + x = 69.245938509 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 = 69.245938509 + -62 Combine like terms: 62 + -62 = 0 0 + x = 69.245938509 + -62 x = 69.245938509 + -62 Combine like terms: 69.245938509 + -62 = 7.245938509 x = 7.245938509 Simplifying x = 7.245938509Subproblem 2
x + 62 = -69.245938509 Simplifying x + 62 = -69.245938509 Reorder the terms: 62 + x = -69.245938509 Solving 62 + x = -69.245938509 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 = -69.245938509 + -62 Combine like terms: 62 + -62 = 0 0 + x = -69.245938509 + -62 x = -69.245938509 + -62 Combine like terms: -69.245938509 + -62 = -131.245938509 x = -131.245938509 Simplifying x = -131.245938509Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.245938509, -131.245938509}
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