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Simplifying 180x + x2 = 45 Solving 180x + x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + 180x + x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 180x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 180x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 180x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 180x + x2 = 0 + 45 180x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 180x + x2 = 45 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 = 45 + 8100 Reorder the terms: 8100 + 180x + x2 = 45 + 8100 Combine like terms: 45 + 8100 = 8145 8100 + 180x + x2 = 8145 Factor a perfect square on the left side: (x + 90)(x + 90) = 8145 Calculate the square root of the right side: 90.249653739 Break this problem into two subproblems by setting (x + 90) equal to 90.249653739 and -90.249653739.Subproblem 1
x + 90 = 90.249653739 Simplifying x + 90 = 90.249653739 Reorder the terms: 90 + x = 90.249653739 Solving 90 + x = 90.249653739 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 = 90.249653739 + -90 Combine like terms: 90 + -90 = 0 0 + x = 90.249653739 + -90 x = 90.249653739 + -90 Combine like terms: 90.249653739 + -90 = 0.249653739 x = 0.249653739 Simplifying x = 0.249653739Subproblem 2
x + 90 = -90.249653739 Simplifying x + 90 = -90.249653739 Reorder the terms: 90 + x = -90.249653739 Solving 90 + x = -90.249653739 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 = -90.249653739 + -90 Combine like terms: 90 + -90 = 0 0 + x = -90.249653739 + -90 x = -90.249653739 + -90 Combine like terms: -90.249653739 + -90 = -180.249653739 x = -180.249653739 Simplifying x = -180.249653739Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.249653739, -180.249653739}
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