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Simplifying x2 + 90x + -900 = 0 Reorder the terms: -900 + 90x + x2 = 0 Solving -900 + 90x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '900' to each side of the equation. -900 + 90x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + 90x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + 90x + x2 = 0 + 900 90x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 90x + x2 = 900 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 = 900 + 2025 Reorder the terms: 2025 + 90x + x2 = 900 + 2025 Combine like terms: 900 + 2025 = 2925 2025 + 90x + x2 = 2925 Factor a perfect square on the left side: (x + 45)(x + 45) = 2925 Calculate the square root of the right side: 54.083269132 Break this problem into two subproblems by setting (x + 45) equal to 54.083269132 and -54.083269132.Subproblem 1
x + 45 = 54.083269132 Simplifying x + 45 = 54.083269132 Reorder the terms: 45 + x = 54.083269132 Solving 45 + x = 54.083269132 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 = 54.083269132 + -45 Combine like terms: 45 + -45 = 0 0 + x = 54.083269132 + -45 x = 54.083269132 + -45 Combine like terms: 54.083269132 + -45 = 9.083269132 x = 9.083269132 Simplifying x = 9.083269132Subproblem 2
x + 45 = -54.083269132 Simplifying x + 45 = -54.083269132 Reorder the terms: 45 + x = -54.083269132 Solving 45 + x = -54.083269132 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 = -54.083269132 + -45 Combine like terms: 45 + -45 = 0 0 + x = -54.083269132 + -45 x = -54.083269132 + -45 Combine like terms: -54.083269132 + -45 = -99.083269132 x = -99.083269132 Simplifying x = -99.083269132Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.083269132, -99.083269132}
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