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Simplifying x(x + 17) = 30 Reorder the terms: x(17 + x) = 30 (17 * x + x * x) = 30 (17x + x2) = 30 Solving 17x + x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 17x + x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 17x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 17x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 17x + x2 = 0 + 30 17x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 17x + x2 = 30 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 30 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 30 + 72.25 Combine like terms: 30 + 72.25 = 102.25 72.25 + 17x + x2 = 102.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 102.25 Calculate the square root of the right side: 10.111874208 Break this problem into two subproblems by setting (x + 8.5) equal to 10.111874208 and -10.111874208.Subproblem 1
x + 8.5 = 10.111874208 Simplifying x + 8.5 = 10.111874208 Reorder the terms: 8.5 + x = 10.111874208 Solving 8.5 + x = 10.111874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 10.111874208 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 10.111874208 + -8.5 x = 10.111874208 + -8.5 Combine like terms: 10.111874208 + -8.5 = 1.611874208 x = 1.611874208 Simplifying x = 1.611874208Subproblem 2
x + 8.5 = -10.111874208 Simplifying x + 8.5 = -10.111874208 Reorder the terms: 8.5 + x = -10.111874208 Solving 8.5 + x = -10.111874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -10.111874208 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -10.111874208 + -8.5 x = -10.111874208 + -8.5 Combine like terms: -10.111874208 + -8.5 = -18.611874208 x = -18.611874208 Simplifying x = -18.611874208Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.611874208, -18.611874208}
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