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Simplifying x2 + 3x + 15 = 115 Reorder the terms: 15 + 3x + x2 = 115 Solving 15 + 3x + x2 = 115 Solving for variable 'x'. Reorder the terms: 15 + -115 + 3x + x2 = 115 + -115 Combine like terms: 15 + -115 = -100 -100 + 3x + x2 = 115 + -115 Combine like terms: 115 + -115 = 0 -100 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 3x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 3x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 3x + x2 = 0 + 100 3x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 3x + x2 = 100 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 100 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 100 + 2.25 Combine like terms: 100 + 2.25 = 102.25 2.25 + 3x + x2 = 102.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 102.25 Calculate the square root of the right side: 10.111874208 Break this problem into two subproblems by setting (x + 1.5) equal to 10.111874208 and -10.111874208.Subproblem 1
x + 1.5 = 10.111874208 Simplifying x + 1.5 = 10.111874208 Reorder the terms: 1.5 + x = 10.111874208 Solving 1.5 + x = 10.111874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 10.111874208 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 10.111874208 + -1.5 x = 10.111874208 + -1.5 Combine like terms: 10.111874208 + -1.5 = 8.611874208 x = 8.611874208 Simplifying x = 8.611874208Subproblem 2
x + 1.5 = -10.111874208 Simplifying x + 1.5 = -10.111874208 Reorder the terms: 1.5 + x = -10.111874208 Solving 1.5 + x = -10.111874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -10.111874208 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -10.111874208 + -1.5 x = -10.111874208 + -1.5 Combine like terms: -10.111874208 + -1.5 = -11.611874208 x = -11.611874208 Simplifying x = -11.611874208Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.611874208, -11.611874208}
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