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Simplifying 199 = x2 + 2x Reorder the terms: 199 = 2x + x2 Solving 199 = 2x + x2 Solving for variable 'x'. Reorder the terms: 199 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 199 + -2x + -1x2 = 0 + x2 + -1x2 199 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 199 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -199 + 2x + x2 = 0 Move the constant term to the right: Add '199' to each side of the equation. -199 + 2x + 199 + x2 = 0 + 199 Reorder the terms: -199 + 199 + 2x + x2 = 0 + 199 Combine like terms: -199 + 199 = 0 0 + 2x + x2 = 0 + 199 2x + x2 = 0 + 199 Combine like terms: 0 + 199 = 199 2x + x2 = 199 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 = 199 + 1 Reorder the terms: 1 + 2x + x2 = 199 + 1 Combine like terms: 199 + 1 = 200 1 + 2x + x2 = 200 Factor a perfect square on the left side: (x + 1)(x + 1) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x + 1) equal to 14.142135624 and -14.142135624.Subproblem 1
x + 1 = 14.142135624 Simplifying x + 1 = 14.142135624 Reorder the terms: 1 + x = 14.142135624 Solving 1 + x = 14.142135624 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 = 14.142135624 + -1 Combine like terms: 1 + -1 = 0 0 + x = 14.142135624 + -1 x = 14.142135624 + -1 Combine like terms: 14.142135624 + -1 = 13.142135624 x = 13.142135624 Simplifying x = 13.142135624Subproblem 2
x + 1 = -14.142135624 Simplifying x + 1 = -14.142135624 Reorder the terms: 1 + x = -14.142135624 Solving 1 + x = -14.142135624 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 = -14.142135624 + -1 Combine like terms: 1 + -1 = 0 0 + x = -14.142135624 + -1 x = -14.142135624 + -1 Combine like terms: -14.142135624 + -1 = -15.142135624 x = -15.142135624 Simplifying x = -15.142135624Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.142135624, -15.142135624}
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