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Simplifying x2 + 152000x + -300000000 = 0 Reorder the terms: -300000000 + 152000x + x2 = 0 Solving -300000000 + 152000x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '300000000' to each side of the equation. -300000000 + 152000x + 300000000 + x2 = 0 + 300000000 Reorder the terms: -300000000 + 300000000 + 152000x + x2 = 0 + 300000000 Combine like terms: -300000000 + 300000000 = 0 0 + 152000x + x2 = 0 + 300000000 152000x + x2 = 0 + 300000000 Combine like terms: 0 + 300000000 = 300000000 152000x + x2 = 300000000 The x term is 152000x. Take half its coefficient (76000). Square it (5776000000) and add it to both sides. Add '5776000000' to each side of the equation. 152000x + 5776000000 + x2 = 300000000 + 5776000000 Reorder the terms: 5776000000 + 152000x + x2 = 300000000 + 5776000000 Combine like terms: 300000000 + 5776000000 = 6076000000 5776000000 + 152000x + x2 = 6076000000 Factor a perfect square on the left side: (x + 76000)(x + 76000) = 6076000000 Calculate the square root of the right side: 77948.70107962 Break this problem into two subproblems by setting (x + 76000) equal to 77948.70107962 and -77948.70107962.Subproblem 1
x + 76000 = 77948.70107962 Simplifying x + 76000 = 77948.70107962 Reorder the terms: 76000 + x = 77948.70107962 Solving 76000 + x = 77948.70107962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-76000' to each side of the equation. 76000 + -76000 + x = 77948.70107962 + -76000 Combine like terms: 76000 + -76000 = 0 0 + x = 77948.70107962 + -76000 x = 77948.70107962 + -76000 Combine like terms: 77948.70107962 + -76000 = 1948.70107962 x = 1948.70107962 Simplifying x = 1948.70107962Subproblem 2
x + 76000 = -77948.70107962 Simplifying x + 76000 = -77948.70107962 Reorder the terms: 76000 + x = -77948.70107962 Solving 76000 + x = -77948.70107962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-76000' to each side of the equation. 76000 + -76000 + x = -77948.70107962 + -76000 Combine like terms: 76000 + -76000 = 0 0 + x = -77948.70107962 + -76000 x = -77948.70107962 + -76000 Combine like terms: -77948.70107962 + -76000 = -153948.70107962 x = -153948.70107962 Simplifying x = -153948.70107962Solution
The solution to the problem is based on the solutions from the subproblems. x = {1948.70107962, -153948.70107962}
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