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Simplifying x2 + 5x + -4 = 180 Reorder the terms: -4 + 5x + x2 = 180 Solving -4 + 5x + x2 = 180 Solving for variable 'x'. Reorder the terms: -4 + -180 + 5x + x2 = 180 + -180 Combine like terms: -4 + -180 = -184 -184 + 5x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -184 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '184' to each side of the equation. -184 + 5x + 184 + x2 = 0 + 184 Reorder the terms: -184 + 184 + 5x + x2 = 0 + 184 Combine like terms: -184 + 184 = 0 0 + 5x + x2 = 0 + 184 5x + x2 = 0 + 184 Combine like terms: 0 + 184 = 184 5x + x2 = 184 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 184 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 184 + 6.25 Combine like terms: 184 + 6.25 = 190.25 6.25 + 5x + x2 = 190.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 190.25 Calculate the square root of the right side: 13.793114224 Break this problem into two subproblems by setting (x + 2.5) equal to 13.793114224 and -13.793114224.Subproblem 1
x + 2.5 = 13.793114224 Simplifying x + 2.5 = 13.793114224 Reorder the terms: 2.5 + x = 13.793114224 Solving 2.5 + x = 13.793114224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 13.793114224 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 13.793114224 + -2.5 x = 13.793114224 + -2.5 Combine like terms: 13.793114224 + -2.5 = 11.293114224 x = 11.293114224 Simplifying x = 11.293114224Subproblem 2
x + 2.5 = -13.793114224 Simplifying x + 2.5 = -13.793114224 Reorder the terms: 2.5 + x = -13.793114224 Solving 2.5 + x = -13.793114224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -13.793114224 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -13.793114224 + -2.5 x = -13.793114224 + -2.5 Combine like terms: -13.793114224 + -2.5 = -16.293114224 x = -16.293114224 Simplifying x = -16.293114224Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.293114224, -16.293114224}
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