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Simplifying 200 = x2 + (x + 4) * 2 Reorder the terms: 200 = x2 + (4 + x) * 2 Reorder the terms for easier multiplication: 200 = x2 + 2(4 + x) 200 = x2 + (4 * 2 + x * 2) 200 = x2 + (8 + 2x) Reorder the terms: 200 = 8 + 2x + x2 Solving 200 = 8 + 2x + x2 Solving for variable 'x'. Combine like terms: 200 + -8 = 192 192 + -2x + -1x2 = 8 + 2x + x2 + -8 + -2x + -1x2 Reorder the terms: 192 + -2x + -1x2 = 8 + -8 + 2x + -2x + x2 + -1x2 Combine like terms: 8 + -8 = 0 192 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 192 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 192 + -2x + -1x2 = 0 + x2 + -1x2 192 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 192 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -192 + 2x + x2 = 0 Move the constant term to the right: Add '192' to each side of the equation. -192 + 2x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + 2x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 2x + x2 = 0 + 192 2x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 2x + x2 = 192 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 = 192 + 1 Reorder the terms: 1 + 2x + x2 = 192 + 1 Combine like terms: 192 + 1 = 193 1 + 2x + x2 = 193 Factor a perfect square on the left side: (x + 1)(x + 1) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (x + 1) equal to 13.892443989 and -13.892443989.Subproblem 1
x + 1 = 13.892443989 Simplifying x + 1 = 13.892443989 Reorder the terms: 1 + x = 13.892443989 Solving 1 + x = 13.892443989 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 = 13.892443989 + -1 Combine like terms: 1 + -1 = 0 0 + x = 13.892443989 + -1 x = 13.892443989 + -1 Combine like terms: 13.892443989 + -1 = 12.892443989 x = 12.892443989 Simplifying x = 12.892443989Subproblem 2
x + 1 = -13.892443989 Simplifying x + 1 = -13.892443989 Reorder the terms: 1 + x = -13.892443989 Solving 1 + x = -13.892443989 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 = -13.892443989 + -1 Combine like terms: 1 + -1 = 0 0 + x = -13.892443989 + -1 x = -13.892443989 + -1 Combine like terms: -13.892443989 + -1 = -14.892443989 x = -14.892443989 Simplifying x = -14.892443989Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.892443989, -14.892443989}
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