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Simplifying 2x2 + -90x + 81 = 0 Reorder the terms: 81 + -90x + 2x2 = 0 Solving 81 + -90x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 40.5 + -45x + x2 = 0 Move the constant term to the right: Add '-40.5' to each side of the equation. 40.5 + -45x + -40.5 + x2 = 0 + -40.5 Reorder the terms: 40.5 + -40.5 + -45x + x2 = 0 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + -45x + x2 = 0 + -40.5 -45x + x2 = 0 + -40.5 Combine like terms: 0 + -40.5 = -40.5 -45x + x2 = -40.5 The x term is -45x. Take half its coefficient (-22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. -45x + 506.25 + x2 = -40.5 + 506.25 Reorder the terms: 506.25 + -45x + x2 = -40.5 + 506.25 Combine like terms: -40.5 + 506.25 = 465.75 506.25 + -45x + x2 = 465.75 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 465.75 Calculate the square root of the right side: 21.581241855 Break this problem into two subproblems by setting (x + -22.5) equal to 21.581241855 and -21.581241855.Subproblem 1
x + -22.5 = 21.581241855 Simplifying x + -22.5 = 21.581241855 Reorder the terms: -22.5 + x = 21.581241855 Solving -22.5 + x = 21.581241855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = 21.581241855 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 21.581241855 + 22.5 x = 21.581241855 + 22.5 Combine like terms: 21.581241855 + 22.5 = 44.081241855 x = 44.081241855 Simplifying x = 44.081241855Subproblem 2
x + -22.5 = -21.581241855 Simplifying x + -22.5 = -21.581241855 Reorder the terms: -22.5 + x = -21.581241855 Solving -22.5 + x = -21.581241855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = -21.581241855 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -21.581241855 + 22.5 x = -21.581241855 + 22.5 Combine like terms: -21.581241855 + 22.5 = 0.918758145 x = 0.918758145 Simplifying x = 0.918758145Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.081241855, 0.918758145}
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