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Simplifying x2 + 4x + -190 = 0 Reorder the terms: -190 + 4x + x2 = 0 Solving -190 + 4x + 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 + 4x + 190 + x2 = 0 + 190 Reorder the terms: -190 + 190 + 4x + x2 = 0 + 190 Combine like terms: -190 + 190 = 0 0 + 4x + x2 = 0 + 190 4x + x2 = 0 + 190 Combine like terms: 0 + 190 = 190 4x + x2 = 190 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 = 190 + 4 Reorder the terms: 4 + 4x + x2 = 190 + 4 Combine like terms: 190 + 4 = 194 4 + 4x + x2 = 194 Factor a perfect square on the left side: (x + 2)(x + 2) = 194 Calculate the square root of the right side: 13.928388277 Break this problem into two subproblems by setting (x + 2) equal to 13.928388277 and -13.928388277.Subproblem 1
x + 2 = 13.928388277 Simplifying x + 2 = 13.928388277 Reorder the terms: 2 + x = 13.928388277 Solving 2 + x = 13.928388277 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 = 13.928388277 + -2 Combine like terms: 2 + -2 = 0 0 + x = 13.928388277 + -2 x = 13.928388277 + -2 Combine like terms: 13.928388277 + -2 = 11.928388277 x = 11.928388277 Simplifying x = 11.928388277Subproblem 2
x + 2 = -13.928388277 Simplifying x + 2 = -13.928388277 Reorder the terms: 2 + x = -13.928388277 Solving 2 + x = -13.928388277 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 = -13.928388277 + -2 Combine like terms: 2 + -2 = 0 0 + x = -13.928388277 + -2 x = -13.928388277 + -2 Combine like terms: -13.928388277 + -2 = -15.928388277 x = -15.928388277 Simplifying x = -15.928388277Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.928388277, -15.928388277}
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