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Simplifying 1x2 + -10x + -240 = 0 Reorder the terms: -240 + -10x + 1x2 = 0 Solving -240 + -10x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + -10x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + -10x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + -10x + x2 = 0 + 240 -10x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 -10x + x2 = 240 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 240 + 25 Reorder the terms: 25 + -10x + x2 = 240 + 25 Combine like terms: 240 + 25 = 265 25 + -10x + x2 = 265 Factor a perfect square on the left side: (x + -5)(x + -5) = 265 Calculate the square root of the right side: 16.278820596 Break this problem into two subproblems by setting (x + -5) equal to 16.278820596 and -16.278820596.Subproblem 1
x + -5 = 16.278820596 Simplifying x + -5 = 16.278820596 Reorder the terms: -5 + x = 16.278820596 Solving -5 + x = 16.278820596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 16.278820596 + 5 Combine like terms: -5 + 5 = 0 0 + x = 16.278820596 + 5 x = 16.278820596 + 5 Combine like terms: 16.278820596 + 5 = 21.278820596 x = 21.278820596 Simplifying x = 21.278820596Subproblem 2
x + -5 = -16.278820596 Simplifying x + -5 = -16.278820596 Reorder the terms: -5 + x = -16.278820596 Solving -5 + x = -16.278820596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -16.278820596 + 5 Combine like terms: -5 + 5 = 0 0 + x = -16.278820596 + 5 x = -16.278820596 + 5 Combine like terms: -16.278820596 + 5 = -11.278820596 x = -11.278820596 Simplifying x = -11.278820596Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.278820596, -11.278820596}
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