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Simplifying 0 = x2 + 2x + -190 Reorder the terms: 0 = -190 + 2x + x2 Solving 0 = -190 + 2x + x2 Solving for variable 'x'. Combine like terms: 0 + 190 = 190 190 + -2x + -1x2 = -190 + 2x + x2 + 190 + -2x + -1x2 Reorder the terms: 190 + -2x + -1x2 = -190 + 190 + 2x + -2x + x2 + -1x2 Combine like terms: -190 + 190 = 0 190 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 190 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 190 + -2x + -1x2 = 0 + x2 + -1x2 190 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 190 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -190 + 2x + x2 = 0 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 = 12.820274961 x = 12.820274961 Simplifying x = 12.820274961Subproblem 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 = -14.820274961 x = -14.820274961 Simplifying x = -14.820274961Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.820274961, -14.820274961}
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