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Simplifying x2 + 4x + -325 = 0 Reorder the terms: -325 + 4x + x2 = 0 Solving -325 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '325' to each side of the equation. -325 + 4x + 325 + x2 = 0 + 325 Reorder the terms: -325 + 325 + 4x + x2 = 0 + 325 Combine like terms: -325 + 325 = 0 0 + 4x + x2 = 0 + 325 4x + x2 = 0 + 325 Combine like terms: 0 + 325 = 325 4x + x2 = 325 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 = 325 + 4 Reorder the terms: 4 + 4x + x2 = 325 + 4 Combine like terms: 325 + 4 = 329 4 + 4x + x2 = 329 Factor a perfect square on the left side: (x + 2)(x + 2) = 329 Calculate the square root of the right side: 18.138357147 Break this problem into two subproblems by setting (x + 2) equal to 18.138357147 and -18.138357147.Subproblem 1
x + 2 = 18.138357147 Simplifying x + 2 = 18.138357147 Reorder the terms: 2 + x = 18.138357147 Solving 2 + x = 18.138357147 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 = 18.138357147 + -2 Combine like terms: 2 + -2 = 0 0 + x = 18.138357147 + -2 x = 18.138357147 + -2 Combine like terms: 18.138357147 + -2 = 16.138357147 x = 16.138357147 Simplifying x = 16.138357147Subproblem 2
x + 2 = -18.138357147 Simplifying x + 2 = -18.138357147 Reorder the terms: 2 + x = -18.138357147 Solving 2 + x = -18.138357147 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 = -18.138357147 + -2 Combine like terms: 2 + -2 = 0 0 + x = -18.138357147 + -2 x = -18.138357147 + -2 Combine like terms: -18.138357147 + -2 = -20.138357147 x = -20.138357147 Simplifying x = -20.138357147Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.138357147, -20.138357147}
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