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Simplifying x2 + 90x + -2000 = 0 Reorder the terms: -2000 + 90x + x2 = 0 Solving -2000 + 90x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2000' to each side of the equation. -2000 + 90x + 2000 + x2 = 0 + 2000 Reorder the terms: -2000 + 2000 + 90x + x2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + 90x + x2 = 0 + 2000 90x + x2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 90x + x2 = 2000 The x term is 90x. Take half its coefficient (45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. 90x + 2025 + x2 = 2000 + 2025 Reorder the terms: 2025 + 90x + x2 = 2000 + 2025 Combine like terms: 2000 + 2025 = 4025 2025 + 90x + x2 = 4025 Factor a perfect square on the left side: (x + 45)(x + 45) = 4025 Calculate the square root of the right side: 63.442887702 Break this problem into two subproblems by setting (x + 45) equal to 63.442887702 and -63.442887702.Subproblem 1
x + 45 = 63.442887702 Simplifying x + 45 = 63.442887702 Reorder the terms: 45 + x = 63.442887702 Solving 45 + x = 63.442887702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = 63.442887702 + -45 Combine like terms: 45 + -45 = 0 0 + x = 63.442887702 + -45 x = 63.442887702 + -45 Combine like terms: 63.442887702 + -45 = 18.442887702 x = 18.442887702 Simplifying x = 18.442887702Subproblem 2
x + 45 = -63.442887702 Simplifying x + 45 = -63.442887702 Reorder the terms: 45 + x = -63.442887702 Solving 45 + x = -63.442887702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = -63.442887702 + -45 Combine like terms: 45 + -45 = 0 0 + x = -63.442887702 + -45 x = -63.442887702 + -45 Combine like terms: -63.442887702 + -45 = -108.442887702 x = -108.442887702 Simplifying x = -108.442887702Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.442887702, -108.442887702}
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