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Simplifying 210 = (x + 2)(x) + 6 Reorder the terms: 210 = (2 + x)(x) + 6 Reorder the terms for easier multiplication: 210 = x(2 + x) + 6 210 = (2 * x + x * x) + 6 210 = (2x + x2) + 6 Reorder the terms: 210 = 6 + 2x + x2 Solving 210 = 6 + 2x + x2 Solving for variable 'x'. Combine like terms: 210 + -6 = 204 204 + -2x + -1x2 = 6 + 2x + x2 + -6 + -2x + -1x2 Reorder the terms: 204 + -2x + -1x2 = 6 + -6 + 2x + -2x + x2 + -1x2 Combine like terms: 6 + -6 = 0 204 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 204 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 204 + -2x + -1x2 = 0 + x2 + -1x2 204 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 204 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -204 + 2x + x2 = 0 Move the constant term to the right: Add '204' to each side of the equation. -204 + 2x + 204 + x2 = 0 + 204 Reorder the terms: -204 + 204 + 2x + x2 = 0 + 204 Combine like terms: -204 + 204 = 0 0 + 2x + x2 = 0 + 204 2x + x2 = 0 + 204 Combine like terms: 0 + 204 = 204 2x + x2 = 204 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 = 204 + 1 Reorder the terms: 1 + 2x + x2 = 204 + 1 Combine like terms: 204 + 1 = 205 1 + 2x + x2 = 205 Factor a perfect square on the left side: (x + 1)(x + 1) = 205 Calculate the square root of the right side: 14.317821063 Break this problem into two subproblems by setting (x + 1) equal to 14.317821063 and -14.317821063.Subproblem 1
x + 1 = 14.317821063 Simplifying x + 1 = 14.317821063 Reorder the terms: 1 + x = 14.317821063 Solving 1 + x = 14.317821063 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 = 14.317821063 + -1 Combine like terms: 1 + -1 = 0 0 + x = 14.317821063 + -1 x = 14.317821063 + -1 Combine like terms: 14.317821063 + -1 = 13.317821063 x = 13.317821063 Simplifying x = 13.317821063Subproblem 2
x + 1 = -14.317821063 Simplifying x + 1 = -14.317821063 Reorder the terms: 1 + x = -14.317821063 Solving 1 + x = -14.317821063 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 = -14.317821063 + -1 Combine like terms: 1 + -1 = 0 0 + x = -14.317821063 + -1 x = -14.317821063 + -1 Combine like terms: -14.317821063 + -1 = -15.317821063 x = -15.317821063 Simplifying x = -15.317821063Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.317821063, -15.317821063}
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