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Simplifying x2 + 157x = 73790 Reorder the terms: 157x + x2 = 73790 Solving 157x + x2 = 73790 Solving for variable 'x'. Reorder the terms: -73790 + 157x + x2 = 73790 + -73790 Combine like terms: 73790 + -73790 = 0 -73790 + 157x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '73790' to each side of the equation. -73790 + 157x + 73790 + x2 = 0 + 73790 Reorder the terms: -73790 + 73790 + 157x + x2 = 0 + 73790 Combine like terms: -73790 + 73790 = 0 0 + 157x + x2 = 0 + 73790 157x + x2 = 0 + 73790 Combine like terms: 0 + 73790 = 73790 157x + x2 = 73790 The x term is 157x. Take half its coefficient (78.5). Square it (6162.25) and add it to both sides. Add '6162.25' to each side of the equation. 157x + 6162.25 + x2 = 73790 + 6162.25 Reorder the terms: 6162.25 + 157x + x2 = 73790 + 6162.25 Combine like terms: 73790 + 6162.25 = 79952.25 6162.25 + 157x + x2 = 79952.25 Factor a perfect square on the left side: (x + 78.5)(x + 78.5) = 79952.25 Calculate the square root of the right side: 282.758289003 Break this problem into two subproblems by setting (x + 78.5) equal to 282.758289003 and -282.758289003.Subproblem 1
x + 78.5 = 282.758289003 Simplifying x + 78.5 = 282.758289003 Reorder the terms: 78.5 + x = 282.758289003 Solving 78.5 + x = 282.758289003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-78.5' to each side of the equation. 78.5 + -78.5 + x = 282.758289003 + -78.5 Combine like terms: 78.5 + -78.5 = 0.0 0.0 + x = 282.758289003 + -78.5 x = 282.758289003 + -78.5 Combine like terms: 282.758289003 + -78.5 = 204.258289003 x = 204.258289003 Simplifying x = 204.258289003Subproblem 2
x + 78.5 = -282.758289003 Simplifying x + 78.5 = -282.758289003 Reorder the terms: 78.5 + x = -282.758289003 Solving 78.5 + x = -282.758289003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-78.5' to each side of the equation. 78.5 + -78.5 + x = -282.758289003 + -78.5 Combine like terms: 78.5 + -78.5 = 0.0 0.0 + x = -282.758289003 + -78.5 x = -282.758289003 + -78.5 Combine like terms: -282.758289003 + -78.5 = -361.258289003 x = -361.258289003 Simplifying x = -361.258289003Solution
The solution to the problem is based on the solutions from the subproblems. x = {204.258289003, -361.258289003}
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