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Simplifying x2 + 7x + -360 = 0 Reorder the terms: -360 + 7x + x2 = 0 Solving -360 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + 7x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + 7x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 7x + x2 = 0 + 360 7x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 7x + x2 = 360 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 360 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 360 + 12.25 Combine like terms: 360 + 12.25 = 372.25 12.25 + 7x + x2 = 372.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 372.25 Calculate the square root of the right side: 19.293781382 Break this problem into two subproblems by setting (x + 3.5) equal to 19.293781382 and -19.293781382.Subproblem 1
x + 3.5 = 19.293781382 Simplifying x + 3.5 = 19.293781382 Reorder the terms: 3.5 + x = 19.293781382 Solving 3.5 + x = 19.293781382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 19.293781382 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 19.293781382 + -3.5 x = 19.293781382 + -3.5 Combine like terms: 19.293781382 + -3.5 = 15.793781382 x = 15.793781382 Simplifying x = 15.793781382Subproblem 2
x + 3.5 = -19.293781382 Simplifying x + 3.5 = -19.293781382 Reorder the terms: 3.5 + x = -19.293781382 Solving 3.5 + x = -19.293781382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -19.293781382 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -19.293781382 + -3.5 x = -19.293781382 + -3.5 Combine like terms: -19.293781382 + -3.5 = -22.793781382 x = -22.793781382 Simplifying x = -22.793781382Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.793781382, -22.793781382}
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