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Simplifying x2 + -3x + -36 = 362 Reorder the terms: -36 + -3x + x2 = 362 Solving -36 + -3x + x2 = 362 Solving for variable 'x'. Reorder the terms: -36 + -362 + -3x + x2 = 362 + -362 Combine like terms: -36 + -362 = -398 -398 + -3x + x2 = 362 + -362 Combine like terms: 362 + -362 = 0 -398 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '398' to each side of the equation. -398 + -3x + 398 + x2 = 0 + 398 Reorder the terms: -398 + 398 + -3x + x2 = 0 + 398 Combine like terms: -398 + 398 = 0 0 + -3x + x2 = 0 + 398 -3x + x2 = 0 + 398 Combine like terms: 0 + 398 = 398 -3x + x2 = 398 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 398 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 398 + 2.25 Combine like terms: 398 + 2.25 = 400.25 2.25 + -3x + x2 = 400.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 400.25 Calculate the square root of the right side: 20.006249024 Break this problem into two subproblems by setting (x + -1.5) equal to 20.006249024 and -20.006249024.Subproblem 1
x + -1.5 = 20.006249024 Simplifying x + -1.5 = 20.006249024 Reorder the terms: -1.5 + x = 20.006249024 Solving -1.5 + x = 20.006249024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 20.006249024 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 20.006249024 + 1.5 x = 20.006249024 + 1.5 Combine like terms: 20.006249024 + 1.5 = 21.506249024 x = 21.506249024 Simplifying x = 21.506249024Subproblem 2
x + -1.5 = -20.006249024 Simplifying x + -1.5 = -20.006249024 Reorder the terms: -1.5 + x = -20.006249024 Solving -1.5 + x = -20.006249024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -20.006249024 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -20.006249024 + 1.5 x = -20.006249024 + 1.5 Combine like terms: -20.006249024 + 1.5 = -18.506249024 x = -18.506249024 Simplifying x = -18.506249024Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.506249024, -18.506249024}
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