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Simplifying x2 + -23x + -240 = 0 Reorder the terms: -240 + -23x + x2 = 0 Solving -240 + -23x + x2 = 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 + -23x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + -23x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + -23x + x2 = 0 + 240 -23x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 -23x + x2 = 240 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = 240 + 132.25 Reorder the terms: 132.25 + -23x + x2 = 240 + 132.25 Combine like terms: 240 + 132.25 = 372.25 132.25 + -23x + x2 = 372.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 372.25 Calculate the square root of the right side: 19.293781382 Break this problem into two subproblems by setting (x + -11.5) equal to 19.293781382 and -19.293781382.Subproblem 1
x + -11.5 = 19.293781382 Simplifying x + -11.5 = 19.293781382 Reorder the terms: -11.5 + x = 19.293781382 Solving -11.5 + x = 19.293781382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 19.293781382 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 19.293781382 + 11.5 x = 19.293781382 + 11.5 Combine like terms: 19.293781382 + 11.5 = 30.793781382 x = 30.793781382 Simplifying x = 30.793781382Subproblem 2
x + -11.5 = -19.293781382 Simplifying x + -11.5 = -19.293781382 Reorder the terms: -11.5 + x = -19.293781382 Solving -11.5 + x = -19.293781382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -19.293781382 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -19.293781382 + 11.5 x = -19.293781382 + 11.5 Combine like terms: -19.293781382 + 11.5 = -7.793781382 x = -7.793781382 Simplifying x = -7.793781382Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.793781382, -7.793781382}
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