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Simplifying x2 + 4x + -184 = 0 Reorder the terms: -184 + 4x + x2 = 0 Solving -184 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '184' to each side of the equation. -184 + 4x + 184 + x2 = 0 + 184 Reorder the terms: -184 + 184 + 4x + x2 = 0 + 184 Combine like terms: -184 + 184 = 0 0 + 4x + x2 = 0 + 184 4x + x2 = 0 + 184 Combine like terms: 0 + 184 = 184 4x + x2 = 184 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 = 184 + 4 Reorder the terms: 4 + 4x + x2 = 184 + 4 Combine like terms: 184 + 4 = 188 4 + 4x + x2 = 188 Factor a perfect square on the left side: (x + 2)(x + 2) = 188 Calculate the square root of the right side: 13.711309201 Break this problem into two subproblems by setting (x + 2) equal to 13.711309201 and -13.711309201.Subproblem 1
x + 2 = 13.711309201 Simplifying x + 2 = 13.711309201 Reorder the terms: 2 + x = 13.711309201 Solving 2 + x = 13.711309201 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 = 13.711309201 + -2 Combine like terms: 2 + -2 = 0 0 + x = 13.711309201 + -2 x = 13.711309201 + -2 Combine like terms: 13.711309201 + -2 = 11.711309201 x = 11.711309201 Simplifying x = 11.711309201Subproblem 2
x + 2 = -13.711309201 Simplifying x + 2 = -13.711309201 Reorder the terms: 2 + x = -13.711309201 Solving 2 + x = -13.711309201 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 = -13.711309201 + -2 Combine like terms: 2 + -2 = 0 0 + x = -13.711309201 + -2 x = -13.711309201 + -2 Combine like terms: -13.711309201 + -2 = -15.711309201 x = -15.711309201 Simplifying x = -15.711309201Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.711309201, -15.711309201}
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