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Simplifying x2 + 5x + -105 = 0 Reorder the terms: -105 + 5x + x2 = 0 Solving -105 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '105' to each side of the equation. -105 + 5x + 105 + x2 = 0 + 105 Reorder the terms: -105 + 105 + 5x + x2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + 5x + x2 = 0 + 105 5x + x2 = 0 + 105 Combine like terms: 0 + 105 = 105 5x + x2 = 105 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 105 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 105 + 6.25 Combine like terms: 105 + 6.25 = 111.25 6.25 + 5x + x2 = 111.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 111.25 Calculate the square root of the right side: 10.547511555 Break this problem into two subproblems by setting (x + 2.5) equal to 10.547511555 and -10.547511555.Subproblem 1
x + 2.5 = 10.547511555 Simplifying x + 2.5 = 10.547511555 Reorder the terms: 2.5 + x = 10.547511555 Solving 2.5 + x = 10.547511555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 10.547511555 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 10.547511555 + -2.5 x = 10.547511555 + -2.5 Combine like terms: 10.547511555 + -2.5 = 8.047511555 x = 8.047511555 Simplifying x = 8.047511555Subproblem 2
x + 2.5 = -10.547511555 Simplifying x + 2.5 = -10.547511555 Reorder the terms: 2.5 + x = -10.547511555 Solving 2.5 + x = -10.547511555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -10.547511555 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -10.547511555 + -2.5 x = -10.547511555 + -2.5 Combine like terms: -10.547511555 + -2.5 = -13.047511555 x = -13.047511555 Simplifying x = -13.047511555Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.047511555, -13.047511555}
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