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Simplifying 200 = x2 + -2x + 1 Reorder the terms: 200 = 1 + -2x + x2 Solving 200 = 1 + -2x + x2 Solving for variable 'x'. Combine like terms: 200 + -1 = 199 199 + 2x + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2 Reorder the terms: 199 + 2x + -1x2 = 1 + -1 + -2x + 2x + x2 + -1x2 Combine like terms: 1 + -1 = 0 199 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2 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 = 15.142135624 x = 15.142135624 Simplifying x = 15.142135624Subproblem 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 = -13.142135624 x = -13.142135624 Simplifying x = -13.142135624Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.142135624, -13.142135624}
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