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Simplifying x2 + 90x = 2925 Reorder the terms: 90x + x2 = 2925 Solving 90x + x2 = 2925 Solving for variable 'x'. Reorder the terms: -2925 + 90x + x2 = 2925 + -2925 Combine like terms: 2925 + -2925 = 0 -2925 + 90x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2925' to each side of the equation. -2925 + 90x + 2925 + x2 = 0 + 2925 Reorder the terms: -2925 + 2925 + 90x + x2 = 0 + 2925 Combine like terms: -2925 + 2925 = 0 0 + 90x + x2 = 0 + 2925 90x + x2 = 0 + 2925 Combine like terms: 0 + 2925 = 2925 90x + x2 = 2925 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 = 2925 + 2025 Reorder the terms: 2025 + 90x + x2 = 2925 + 2025 Combine like terms: 2925 + 2025 = 4950 2025 + 90x + x2 = 4950 Factor a perfect square on the left side: (x + 45)(x + 45) = 4950 Calculate the square root of the right side: 70.356236397 Break this problem into two subproblems by setting (x + 45) equal to 70.356236397 and -70.356236397.Subproblem 1
x + 45 = 70.356236397 Simplifying x + 45 = 70.356236397 Reorder the terms: 45 + x = 70.356236397 Solving 45 + x = 70.356236397 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 = 70.356236397 + -45 Combine like terms: 45 + -45 = 0 0 + x = 70.356236397 + -45 x = 70.356236397 + -45 Combine like terms: 70.356236397 + -45 = 25.356236397 x = 25.356236397 Simplifying x = 25.356236397Subproblem 2
x + 45 = -70.356236397 Simplifying x + 45 = -70.356236397 Reorder the terms: 45 + x = -70.356236397 Solving 45 + x = -70.356236397 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 = -70.356236397 + -45 Combine like terms: 45 + -45 = 0 0 + x = -70.356236397 + -45 x = -70.356236397 + -45 Combine like terms: -70.356236397 + -45 = -115.356236397 x = -115.356236397 Simplifying x = -115.356236397Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.356236397, -115.356236397}
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