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Simplifying -1x2 + 90x + -54 = 0 Reorder the terms: -54 + 90x + -1x2 = 0 Solving -54 + 90x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 54 + -90x + x2 = 0 Move the constant term to the right: Add '-54' to each side of the equation. 54 + -90x + -54 + x2 = 0 + -54 Reorder the terms: 54 + -54 + -90x + x2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + -90x + x2 = 0 + -54 -90x + x2 = 0 + -54 Combine like terms: 0 + -54 = -54 -90x + x2 = -54 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 = -54 + 2025 Reorder the terms: 2025 + -90x + x2 = -54 + 2025 Combine like terms: -54 + 2025 = 1971 2025 + -90x + x2 = 1971 Factor a perfect square on the left side: (x + -45)(x + -45) = 1971 Calculate the square root of the right side: 44.395945761 Break this problem into two subproblems by setting (x + -45) equal to 44.395945761 and -44.395945761.Subproblem 1
x + -45 = 44.395945761 Simplifying x + -45 = 44.395945761 Reorder the terms: -45 + x = 44.395945761 Solving -45 + x = 44.395945761 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 = 44.395945761 + 45 Combine like terms: -45 + 45 = 0 0 + x = 44.395945761 + 45 x = 44.395945761 + 45 Combine like terms: 44.395945761 + 45 = 89.395945761 x = 89.395945761 Simplifying x = 89.395945761Subproblem 2
x + -45 = -44.395945761 Simplifying x + -45 = -44.395945761 Reorder the terms: -45 + x = -44.395945761 Solving -45 + x = -44.395945761 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 = -44.395945761 + 45 Combine like terms: -45 + 45 = 0 0 + x = -44.395945761 + 45 x = -44.395945761 + 45 Combine like terms: -44.395945761 + 45 = 0.604054239 x = 0.604054239 Simplifying x = 0.604054239Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.395945761, 0.604054239}
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