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Simplifying x2 + -300x + 17980 = 0 Reorder the terms: 17980 + -300x + x2 = 0 Solving 17980 + -300x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-17980' to each side of the equation. 17980 + -300x + -17980 + x2 = 0 + -17980 Reorder the terms: 17980 + -17980 + -300x + x2 = 0 + -17980 Combine like terms: 17980 + -17980 = 0 0 + -300x + x2 = 0 + -17980 -300x + x2 = 0 + -17980 Combine like terms: 0 + -17980 = -17980 -300x + x2 = -17980 The x term is -300x. Take half its coefficient (-150). Square it (22500) and add it to both sides. Add '22500' to each side of the equation. -300x + 22500 + x2 = -17980 + 22500 Reorder the terms: 22500 + -300x + x2 = -17980 + 22500 Combine like terms: -17980 + 22500 = 4520 22500 + -300x + x2 = 4520 Factor a perfect square on the left side: (x + -150)(x + -150) = 4520 Calculate the square root of the right side: 67.230945256 Break this problem into two subproblems by setting (x + -150) equal to 67.230945256 and -67.230945256.Subproblem 1
x + -150 = 67.230945256 Simplifying x + -150 = 67.230945256 Reorder the terms: -150 + x = 67.230945256 Solving -150 + x = 67.230945256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = 67.230945256 + 150 Combine like terms: -150 + 150 = 0 0 + x = 67.230945256 + 150 x = 67.230945256 + 150 Combine like terms: 67.230945256 + 150 = 217.230945256 x = 217.230945256 Simplifying x = 217.230945256Subproblem 2
x + -150 = -67.230945256 Simplifying x + -150 = -67.230945256 Reorder the terms: -150 + x = -67.230945256 Solving -150 + x = -67.230945256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = -67.230945256 + 150 Combine like terms: -150 + 150 = 0 0 + x = -67.230945256 + 150 x = -67.230945256 + 150 Combine like terms: -67.230945256 + 150 = 82.769054744 x = 82.769054744 Simplifying x = 82.769054744Solution
The solution to the problem is based on the solutions from the subproblems. x = {217.230945256, 82.769054744}
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