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Simplifying x2 + x + -190 = 0 Reorder the terms: -190 + x + x2 = 0 Solving -190 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '190' to each side of the equation. -190 + x + 190 + x2 = 0 + 190 Reorder the terms: -190 + 190 + x + x2 = 0 + 190 Combine like terms: -190 + 190 = 0 0 + x + x2 = 0 + 190 x + x2 = 0 + 190 Combine like terms: 0 + 190 = 190 x + x2 = 190 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 190 + 0.25 Reorder the terms: 0.25 + x + x2 = 190 + 0.25 Combine like terms: 190 + 0.25 = 190.25 0.25 + x + x2 = 190.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 190.25 Calculate the square root of the right side: 13.793114224 Break this problem into two subproblems by setting (x + 0.5) equal to 13.793114224 and -13.793114224.Subproblem 1
x + 0.5 = 13.793114224 Simplifying x + 0.5 = 13.793114224 Reorder the terms: 0.5 + x = 13.793114224 Solving 0.5 + x = 13.793114224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 13.793114224 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 13.793114224 + -0.5 x = 13.793114224 + -0.5 Combine like terms: 13.793114224 + -0.5 = 13.293114224 x = 13.293114224 Simplifying x = 13.293114224Subproblem 2
x + 0.5 = -13.793114224 Simplifying x + 0.5 = -13.793114224 Reorder the terms: 0.5 + x = -13.793114224 Solving 0.5 + x = -13.793114224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -13.793114224 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -13.793114224 + -0.5 x = -13.793114224 + -0.5 Combine like terms: -13.793114224 + -0.5 = -14.293114224 x = -14.293114224 Simplifying x = -14.293114224Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.293114224, -14.293114224}
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