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Simplifying x2 = 114x + 399 Reorder the terms: x2 = 399 + 114x Solving x2 = 399 + 114x Solving for variable 'x'. Reorder the terms: -399 + -114x + x2 = 399 + 114x + -399 + -114x Reorder the terms: -399 + -114x + x2 = 399 + -399 + 114x + -114x Combine like terms: 399 + -399 = 0 -399 + -114x + x2 = 0 + 114x + -114x -399 + -114x + x2 = 114x + -114x Combine like terms: 114x + -114x = 0 -399 + -114x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '399' to each side of the equation. -399 + -114x + 399 + x2 = 0 + 399 Reorder the terms: -399 + 399 + -114x + x2 = 0 + 399 Combine like terms: -399 + 399 = 0 0 + -114x + x2 = 0 + 399 -114x + x2 = 0 + 399 Combine like terms: 0 + 399 = 399 -114x + x2 = 399 The x term is -114x. Take half its coefficient (-57). Square it (3249) and add it to both sides. Add '3249' to each side of the equation. -114x + 3249 + x2 = 399 + 3249 Reorder the terms: 3249 + -114x + x2 = 399 + 3249 Combine like terms: 399 + 3249 = 3648 3249 + -114x + x2 = 3648 Factor a perfect square on the left side: (x + -57)(x + -57) = 3648 Calculate the square root of the right side: 60.398675482 Break this problem into two subproblems by setting (x + -57) equal to 60.398675482 and -60.398675482.Subproblem 1
x + -57 = 60.398675482 Simplifying x + -57 = 60.398675482 Reorder the terms: -57 + x = 60.398675482 Solving -57 + x = 60.398675482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '57' to each side of the equation. -57 + 57 + x = 60.398675482 + 57 Combine like terms: -57 + 57 = 0 0 + x = 60.398675482 + 57 x = 60.398675482 + 57 Combine like terms: 60.398675482 + 57 = 117.398675482 x = 117.398675482 Simplifying x = 117.398675482Subproblem 2
x + -57 = -60.398675482 Simplifying x + -57 = -60.398675482 Reorder the terms: -57 + x = -60.398675482 Solving -57 + x = -60.398675482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '57' to each side of the equation. -57 + 57 + x = -60.398675482 + 57 Combine like terms: -57 + 57 = 0 0 + x = -60.398675482 + 57 x = -60.398675482 + 57 Combine like terms: -60.398675482 + 57 = -3.398675482 x = -3.398675482 Simplifying x = -3.398675482Solution
The solution to the problem is based on the solutions from the subproblems. x = {117.398675482, -3.398675482}
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