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Simplifying x2 + 180x + 1160 = 0 Reorder the terms: 1160 + 180x + x2 = 0 Solving 1160 + 180x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1160' to each side of the equation. 1160 + 180x + -1160 + x2 = 0 + -1160 Reorder the terms: 1160 + -1160 + 180x + x2 = 0 + -1160 Combine like terms: 1160 + -1160 = 0 0 + 180x + x2 = 0 + -1160 180x + x2 = 0 + -1160 Combine like terms: 0 + -1160 = -1160 180x + x2 = -1160 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 = -1160 + 8100 Reorder the terms: 8100 + 180x + x2 = -1160 + 8100 Combine like terms: -1160 + 8100 = 6940 8100 + 180x + x2 = 6940 Factor a perfect square on the left side: (x + 90)(x + 90) = 6940 Calculate the square root of the right side: 83.306662399 Break this problem into two subproblems by setting (x + 90) equal to 83.306662399 and -83.306662399.Subproblem 1
x + 90 = 83.306662399 Simplifying x + 90 = 83.306662399 Reorder the terms: 90 + x = 83.306662399 Solving 90 + x = 83.306662399 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 = 83.306662399 + -90 Combine like terms: 90 + -90 = 0 0 + x = 83.306662399 + -90 x = 83.306662399 + -90 Combine like terms: 83.306662399 + -90 = -6.693337601 x = -6.693337601 Simplifying x = -6.693337601Subproblem 2
x + 90 = -83.306662399 Simplifying x + 90 = -83.306662399 Reorder the terms: 90 + x = -83.306662399 Solving 90 + x = -83.306662399 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 = -83.306662399 + -90 Combine like terms: 90 + -90 = 0 0 + x = -83.306662399 + -90 x = -83.306662399 + -90 Combine like terms: -83.306662399 + -90 = -173.306662399 x = -173.306662399 Simplifying x = -173.306662399Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.693337601, -173.306662399}
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