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Simplifying x2 + -690x = 1248 Reorder the terms: -690x + x2 = 1248 Solving -690x + x2 = 1248 Solving for variable 'x'. Reorder the terms: -1248 + -690x + x2 = 1248 + -1248 Combine like terms: 1248 + -1248 = 0 -1248 + -690x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1248' to each side of the equation. -1248 + -690x + 1248 + x2 = 0 + 1248 Reorder the terms: -1248 + 1248 + -690x + x2 = 0 + 1248 Combine like terms: -1248 + 1248 = 0 0 + -690x + x2 = 0 + 1248 -690x + x2 = 0 + 1248 Combine like terms: 0 + 1248 = 1248 -690x + x2 = 1248 The x term is -690x. Take half its coefficient (-345). Square it (119025) and add it to both sides. Add '119025' to each side of the equation. -690x + 119025 + x2 = 1248 + 119025 Reorder the terms: 119025 + -690x + x2 = 1248 + 119025 Combine like terms: 1248 + 119025 = 120273 119025 + -690x + x2 = 120273 Factor a perfect square on the left side: (x + -345)(x + -345) = 120273 Calculate the square root of the right side: 346.803979216 Break this problem into two subproblems by setting (x + -345) equal to 346.803979216 and -346.803979216.Subproblem 1
x + -345 = 346.803979216 Simplifying x + -345 = 346.803979216 Reorder the terms: -345 + x = 346.803979216 Solving -345 + x = 346.803979216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '345' to each side of the equation. -345 + 345 + x = 346.803979216 + 345 Combine like terms: -345 + 345 = 0 0 + x = 346.803979216 + 345 x = 346.803979216 + 345 Combine like terms: 346.803979216 + 345 = 691.803979216 x = 691.803979216 Simplifying x = 691.803979216Subproblem 2
x + -345 = -346.803979216 Simplifying x + -345 = -346.803979216 Reorder the terms: -345 + x = -346.803979216 Solving -345 + x = -346.803979216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '345' to each side of the equation. -345 + 345 + x = -346.803979216 + 345 Combine like terms: -345 + 345 = 0 0 + x = -346.803979216 + 345 x = -346.803979216 + 345 Combine like terms: -346.803979216 + 345 = -1.803979216 x = -1.803979216 Simplifying x = -1.803979216Solution
The solution to the problem is based on the solutions from the subproblems. x = {691.803979216, -1.803979216}
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