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Simplifying x2 + 4x + 2 = 365 Reorder the terms: 2 + 4x + x2 = 365 Solving 2 + 4x + x2 = 365 Solving for variable 'x'. Reorder the terms: 2 + -365 + 4x + x2 = 365 + -365 Combine like terms: 2 + -365 = -363 -363 + 4x + x2 = 365 + -365 Combine like terms: 365 + -365 = 0 -363 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '363' to each side of the equation. -363 + 4x + 363 + x2 = 0 + 363 Reorder the terms: -363 + 363 + 4x + x2 = 0 + 363 Combine like terms: -363 + 363 = 0 0 + 4x + x2 = 0 + 363 4x + x2 = 0 + 363 Combine like terms: 0 + 363 = 363 4x + x2 = 363 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 363 + 4 Reorder the terms: 4 + 4x + x2 = 363 + 4 Combine like terms: 363 + 4 = 367 4 + 4x + x2 = 367 Factor a perfect square on the left side: (x + 2)(x + 2) = 367 Calculate the square root of the right side: 19.157244061 Break this problem into two subproblems by setting (x + 2) equal to 19.157244061 and -19.157244061.Subproblem 1
x + 2 = 19.157244061 Simplifying x + 2 = 19.157244061 Reorder the terms: 2 + x = 19.157244061 Solving 2 + x = 19.157244061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 19.157244061 + -2 Combine like terms: 2 + -2 = 0 0 + x = 19.157244061 + -2 x = 19.157244061 + -2 Combine like terms: 19.157244061 + -2 = 17.157244061 x = 17.157244061 Simplifying x = 17.157244061Subproblem 2
x + 2 = -19.157244061 Simplifying x + 2 = -19.157244061 Reorder the terms: 2 + x = -19.157244061 Solving 2 + x = -19.157244061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -19.157244061 + -2 Combine like terms: 2 + -2 = 0 0 + x = -19.157244061 + -2 x = -19.157244061 + -2 Combine like terms: -19.157244061 + -2 = -21.157244061 x = -21.157244061 Simplifying x = -21.157244061Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.157244061, -21.157244061}
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