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Simplifying x2 + 10x + -10 = 180 Reorder the terms: -10 + 10x + x2 = 180 Solving -10 + 10x + x2 = 180 Solving for variable 'x'. Reorder the terms: -10 + -180 + 10x + x2 = 180 + -180 Combine like terms: -10 + -180 = -190 -190 + 10x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -190 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '190' to each side of the equation. -190 + 10x + 190 + x2 = 0 + 190 Reorder the terms: -190 + 190 + 10x + x2 = 0 + 190 Combine like terms: -190 + 190 = 0 0 + 10x + x2 = 0 + 190 10x + x2 = 0 + 190 Combine like terms: 0 + 190 = 190 10x + x2 = 190 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 = 190 + 25 Reorder the terms: 25 + 10x + x2 = 190 + 25 Combine like terms: 190 + 25 = 215 25 + 10x + x2 = 215 Factor a perfect square on the left side: (x + 5)(x + 5) = 215 Calculate the square root of the right side: 14.662878299 Break this problem into two subproblems by setting (x + 5) equal to 14.662878299 and -14.662878299.Subproblem 1
x + 5 = 14.662878299 Simplifying x + 5 = 14.662878299 Reorder the terms: 5 + x = 14.662878299 Solving 5 + x = 14.662878299 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 = 14.662878299 + -5 Combine like terms: 5 + -5 = 0 0 + x = 14.662878299 + -5 x = 14.662878299 + -5 Combine like terms: 14.662878299 + -5 = 9.662878299 x = 9.662878299 Simplifying x = 9.662878299Subproblem 2
x + 5 = -14.662878299 Simplifying x + 5 = -14.662878299 Reorder the terms: 5 + x = -14.662878299 Solving 5 + x = -14.662878299 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 = -14.662878299 + -5 Combine like terms: 5 + -5 = 0 0 + x = -14.662878299 + -5 x = -14.662878299 + -5 Combine like terms: -14.662878299 + -5 = -19.662878299 x = -19.662878299 Simplifying x = -19.662878299Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.662878299, -19.662878299}
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