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Simplifying x2 + -2x + -190 = 0 Reorder the terms: -190 + -2x + x2 = 0 Solving -190 + -2x + 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 + -2x + 190 + x2 = 0 + 190 Reorder the terms: -190 + 190 + -2x + x2 = 0 + 190 Combine like terms: -190 + 190 = 0 0 + -2x + x2 = 0 + 190 -2x + x2 = 0 + 190 Combine like terms: 0 + 190 = 190 -2x + x2 = 190 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 190 + 1 Reorder the terms: 1 + -2x + x2 = 190 + 1 Combine like terms: 190 + 1 = 191 1 + -2x + x2 = 191 Factor a perfect square on the left side: (x + -1)(x + -1) = 191 Calculate the square root of the right side: 13.820274961 Break this problem into two subproblems by setting (x + -1) equal to 13.820274961 and -13.820274961.Subproblem 1
x + -1 = 13.820274961 Simplifying x + -1 = 13.820274961 Reorder the terms: -1 + x = 13.820274961 Solving -1 + x = 13.820274961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 13.820274961 + 1 Combine like terms: -1 + 1 = 0 0 + x = 13.820274961 + 1 x = 13.820274961 + 1 Combine like terms: 13.820274961 + 1 = 14.820274961 x = 14.820274961 Simplifying x = 14.820274961Subproblem 2
x + -1 = -13.820274961 Simplifying x + -1 = -13.820274961 Reorder the terms: -1 + x = -13.820274961 Solving -1 + x = -13.820274961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -13.820274961 + 1 Combine like terms: -1 + 1 = 0 0 + x = -13.820274961 + 1 x = -13.820274961 + 1 Combine like terms: -13.820274961 + 1 = -12.820274961 x = -12.820274961 Simplifying x = -12.820274961Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.820274961, -12.820274961}
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