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Simplifying x2 + 4x + -178 = 0 Reorder the terms: -178 + 4x + x2 = 0 Solving -178 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '178' to each side of the equation. -178 + 4x + 178 + x2 = 0 + 178 Reorder the terms: -178 + 178 + 4x + x2 = 0 + 178 Combine like terms: -178 + 178 = 0 0 + 4x + x2 = 0 + 178 4x + x2 = 0 + 178 Combine like terms: 0 + 178 = 178 4x + x2 = 178 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 = 178 + 4 Reorder the terms: 4 + 4x + x2 = 178 + 4 Combine like terms: 178 + 4 = 182 4 + 4x + x2 = 182 Factor a perfect square on the left side: (x + 2)(x + 2) = 182 Calculate the square root of the right side: 13.490737563 Break this problem into two subproblems by setting (x + 2) equal to 13.490737563 and -13.490737563.Subproblem 1
x + 2 = 13.490737563 Simplifying x + 2 = 13.490737563 Reorder the terms: 2 + x = 13.490737563 Solving 2 + x = 13.490737563 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 = 13.490737563 + -2 Combine like terms: 2 + -2 = 0 0 + x = 13.490737563 + -2 x = 13.490737563 + -2 Combine like terms: 13.490737563 + -2 = 11.490737563 x = 11.490737563 Simplifying x = 11.490737563Subproblem 2
x + 2 = -13.490737563 Simplifying x + 2 = -13.490737563 Reorder the terms: 2 + x = -13.490737563 Solving 2 + x = -13.490737563 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 = -13.490737563 + -2 Combine like terms: 2 + -2 = 0 0 + x = -13.490737563 + -2 x = -13.490737563 + -2 Combine like terms: -13.490737563 + -2 = -15.490737563 x = -15.490737563 Simplifying x = -15.490737563Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.490737563, -15.490737563}
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