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Simplifying x2 + 4x + -345 = 0 Reorder the terms: -345 + 4x + x2 = 0 Solving -345 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '345' to each side of the equation. -345 + 4x + 345 + x2 = 0 + 345 Reorder the terms: -345 + 345 + 4x + x2 = 0 + 345 Combine like terms: -345 + 345 = 0 0 + 4x + x2 = 0 + 345 4x + x2 = 0 + 345 Combine like terms: 0 + 345 = 345 4x + x2 = 345 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 = 345 + 4 Reorder the terms: 4 + 4x + x2 = 345 + 4 Combine like terms: 345 + 4 = 349 4 + 4x + x2 = 349 Factor a perfect square on the left side: (x + 2)(x + 2) = 349 Calculate the square root of the right side: 18.681541692 Break this problem into two subproblems by setting (x + 2) equal to 18.681541692 and -18.681541692.Subproblem 1
x + 2 = 18.681541692 Simplifying x + 2 = 18.681541692 Reorder the terms: 2 + x = 18.681541692 Solving 2 + x = 18.681541692 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 = 18.681541692 + -2 Combine like terms: 2 + -2 = 0 0 + x = 18.681541692 + -2 x = 18.681541692 + -2 Combine like terms: 18.681541692 + -2 = 16.681541692 x = 16.681541692 Simplifying x = 16.681541692Subproblem 2
x + 2 = -18.681541692 Simplifying x + 2 = -18.681541692 Reorder the terms: 2 + x = -18.681541692 Solving 2 + x = -18.681541692 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 = -18.681541692 + -2 Combine like terms: 2 + -2 = 0 0 + x = -18.681541692 + -2 x = -18.681541692 + -2 Combine like terms: -18.681541692 + -2 = -20.681541692 x = -20.681541692 Simplifying x = -20.681541692Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.681541692, -20.681541692}
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