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Simplifying x2 + -90x + 1000 = 0 Reorder the terms: 1000 + -90x + x2 = 0 Solving 1000 + -90x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1000' to each side of the equation. 1000 + -90x + -1000 + x2 = 0 + -1000 Reorder the terms: 1000 + -1000 + -90x + x2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + -90x + x2 = 0 + -1000 -90x + x2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 -90x + x2 = -1000 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 = -1000 + 2025 Reorder the terms: 2025 + -90x + x2 = -1000 + 2025 Combine like terms: -1000 + 2025 = 1025 2025 + -90x + x2 = 1025 Factor a perfect square on the left side: (x + -45)(x + -45) = 1025 Calculate the square root of the right side: 32.015621187 Break this problem into two subproblems by setting (x + -45) equal to 32.015621187 and -32.015621187.Subproblem 1
x + -45 = 32.015621187 Simplifying x + -45 = 32.015621187 Reorder the terms: -45 + x = 32.015621187 Solving -45 + x = 32.015621187 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 = 32.015621187 + 45 Combine like terms: -45 + 45 = 0 0 + x = 32.015621187 + 45 x = 32.015621187 + 45 Combine like terms: 32.015621187 + 45 = 77.015621187 x = 77.015621187 Simplifying x = 77.015621187Subproblem 2
x + -45 = -32.015621187 Simplifying x + -45 = -32.015621187 Reorder the terms: -45 + x = -32.015621187 Solving -45 + x = -32.015621187 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 = -32.015621187 + 45 Combine like terms: -45 + 45 = 0 0 + x = -32.015621187 + 45 x = -32.015621187 + 45 Combine like terms: -32.015621187 + 45 = 12.984378813 x = 12.984378813 Simplifying x = 12.984378813Solution
The solution to the problem is based on the solutions from the subproblems. x = {77.015621187, 12.984378813}
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