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Simplifying x2 + -90x + -3500 = 0 Reorder the terms: -3500 + -90x + x2 = 0 Solving -3500 + -90x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3500' to each side of the equation. -3500 + -90x + 3500 + x2 = 0 + 3500 Reorder the terms: -3500 + 3500 + -90x + x2 = 0 + 3500 Combine like terms: -3500 + 3500 = 0 0 + -90x + x2 = 0 + 3500 -90x + x2 = 0 + 3500 Combine like terms: 0 + 3500 = 3500 -90x + x2 = 3500 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 = 3500 + 2025 Reorder the terms: 2025 + -90x + x2 = 3500 + 2025 Combine like terms: 3500 + 2025 = 5525 2025 + -90x + x2 = 5525 Factor a perfect square on the left side: (x + -45)(x + -45) = 5525 Calculate the square root of the right side: 74.330343737 Break this problem into two subproblems by setting (x + -45) equal to 74.330343737 and -74.330343737.Subproblem 1
x + -45 = 74.330343737 Simplifying x + -45 = 74.330343737 Reorder the terms: -45 + x = 74.330343737 Solving -45 + x = 74.330343737 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 = 74.330343737 + 45 Combine like terms: -45 + 45 = 0 0 + x = 74.330343737 + 45 x = 74.330343737 + 45 Combine like terms: 74.330343737 + 45 = 119.330343737 x = 119.330343737 Simplifying x = 119.330343737Subproblem 2
x + -45 = -74.330343737 Simplifying x + -45 = -74.330343737 Reorder the terms: -45 + x = -74.330343737 Solving -45 + x = -74.330343737 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 = -74.330343737 + 45 Combine like terms: -45 + 45 = 0 0 + x = -74.330343737 + 45 x = -74.330343737 + 45 Combine like terms: -74.330343737 + 45 = -29.330343737 x = -29.330343737 Simplifying x = -29.330343737Solution
The solution to the problem is based on the solutions from the subproblems. x = {119.330343737, -29.330343737}
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