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Simplifying 210 = (x + 2)(x + 6) Reorder the terms: 210 = (2 + x)(x + 6) Reorder the terms: 210 = (2 + x)(6 + x) Multiply (2 + x) * (6 + x) 210 = (2(6 + x) + x(6 + x)) 210 = ((6 * 2 + x * 2) + x(6 + x)) 210 = ((12 + 2x) + x(6 + x)) 210 = (12 + 2x + (6 * x + x * x)) 210 = (12 + 2x + (6x + x2)) Combine like terms: 2x + 6x = 8x 210 = (12 + 8x + x2) Solving 210 = 12 + 8x + x2 Solving for variable 'x'. Combine like terms: 210 + -12 = 198 198 + -8x + -1x2 = 12 + 8x + x2 + -12 + -8x + -1x2 Reorder the terms: 198 + -8x + -1x2 = 12 + -12 + 8x + -8x + x2 + -1x2 Combine like terms: 12 + -12 = 0 198 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2 198 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 198 + -8x + -1x2 = 0 + x2 + -1x2 198 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 198 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -198 + 8x + x2 = 0 Move the constant term to the right: Add '198' to each side of the equation. -198 + 8x + 198 + x2 = 0 + 198 Reorder the terms: -198 + 198 + 8x + x2 = 0 + 198 Combine like terms: -198 + 198 = 0 0 + 8x + x2 = 0 + 198 8x + x2 = 0 + 198 Combine like terms: 0 + 198 = 198 8x + x2 = 198 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 198 + 16 Reorder the terms: 16 + 8x + x2 = 198 + 16 Combine like terms: 198 + 16 = 214 16 + 8x + x2 = 214 Factor a perfect square on the left side: (x + 4)(x + 4) = 214 Calculate the square root of the right side: 14.628738838 Break this problem into two subproblems by setting (x + 4) equal to 14.628738838 and -14.628738838.Subproblem 1
x + 4 = 14.628738838 Simplifying x + 4 = 14.628738838 Reorder the terms: 4 + x = 14.628738838 Solving 4 + x = 14.628738838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 14.628738838 + -4 Combine like terms: 4 + -4 = 0 0 + x = 14.628738838 + -4 x = 14.628738838 + -4 Combine like terms: 14.628738838 + -4 = 10.628738838 x = 10.628738838 Simplifying x = 10.628738838Subproblem 2
x + 4 = -14.628738838 Simplifying x + 4 = -14.628738838 Reorder the terms: 4 + x = -14.628738838 Solving 4 + x = -14.628738838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -14.628738838 + -4 Combine like terms: 4 + -4 = 0 0 + x = -14.628738838 + -4 x = -14.628738838 + -4 Combine like terms: -14.628738838 + -4 = -18.628738838 x = -18.628738838 Simplifying x = -18.628738838Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.628738838, -18.628738838}
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