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Simplifying x2 + 180x + -360 = 0 Reorder the terms: -360 + 180x + x2 = 0 Solving -360 + 180x + 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 + 180x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + 180x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 180x + x2 = 0 + 360 180x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 180x + x2 = 360 The x term is 180x. Take half its coefficient (90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. 180x + 8100 + x2 = 360 + 8100 Reorder the terms: 8100 + 180x + x2 = 360 + 8100 Combine like terms: 360 + 8100 = 8460 8100 + 180x + x2 = 8460 Factor a perfect square on the left side: (x + 90)(x + 90) = 8460 Calculate the square root of the right side: 91.978258301 Break this problem into two subproblems by setting (x + 90) equal to 91.978258301 and -91.978258301.Subproblem 1
x + 90 = 91.978258301 Simplifying x + 90 = 91.978258301 Reorder the terms: 90 + x = 91.978258301 Solving 90 + x = 91.978258301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-90' to each side of the equation. 90 + -90 + x = 91.978258301 + -90 Combine like terms: 90 + -90 = 0 0 + x = 91.978258301 + -90 x = 91.978258301 + -90 Combine like terms: 91.978258301 + -90 = 1.978258301 x = 1.978258301 Simplifying x = 1.978258301Subproblem 2
x + 90 = -91.978258301 Simplifying x + 90 = -91.978258301 Reorder the terms: 90 + x = -91.978258301 Solving 90 + x = -91.978258301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-90' to each side of the equation. 90 + -90 + x = -91.978258301 + -90 Combine like terms: 90 + -90 = 0 0 + x = -91.978258301 + -90 x = -91.978258301 + -90 Combine like terms: -91.978258301 + -90 = -181.978258301 x = -181.978258301 Simplifying x = -181.978258301Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.978258301, -181.978258301}
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