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Simplifying x2 + 10x + -180 = 0 Reorder the terms: -180 + 10x + x2 = 0 Solving -180 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 10x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 10x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 10x + x2 = 0 + 180 10x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 10x + x2 = 180 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 = 180 + 25 Reorder the terms: 25 + 10x + x2 = 180 + 25 Combine like terms: 180 + 25 = 205 25 + 10x + x2 = 205 Factor a perfect square on the left side: (x + 5)(x + 5) = 205 Calculate the square root of the right side: 14.317821063 Break this problem into two subproblems by setting (x + 5) equal to 14.317821063 and -14.317821063.Subproblem 1
x + 5 = 14.317821063 Simplifying x + 5 = 14.317821063 Reorder the terms: 5 + x = 14.317821063 Solving 5 + x = 14.317821063 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 = 14.317821063 + -5 Combine like terms: 5 + -5 = 0 0 + x = 14.317821063 + -5 x = 14.317821063 + -5 Combine like terms: 14.317821063 + -5 = 9.317821063 x = 9.317821063 Simplifying x = 9.317821063Subproblem 2
x + 5 = -14.317821063 Simplifying x + 5 = -14.317821063 Reorder the terms: 5 + x = -14.317821063 Solving 5 + x = -14.317821063 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 = -14.317821063 + -5 Combine like terms: 5 + -5 = 0 0 + x = -14.317821063 + -5 x = -14.317821063 + -5 Combine like terms: -14.317821063 + -5 = -19.317821063 x = -19.317821063 Simplifying x = -19.317821063Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.317821063, -19.317821063}
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