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Simplifying (20x2) + -18x + -81 = 0 Reorder the terms: -81 + -18x + (20x2) = 0 Solving -81 + -18x + (20x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -4.05 + -0.9x + x2 = 0 Move the constant term to the right: Add '4.05' to each side of the equation. -4.05 + -0.9x + 4.05 + x2 = 0 + 4.05 Reorder the terms: -4.05 + 4.05 + -0.9x + x2 = 0 + 4.05 Combine like terms: -4.05 + 4.05 = 0.00 0.00 + -0.9x + x2 = 0 + 4.05 -0.9x + x2 = 0 + 4.05 Combine like terms: 0 + 4.05 = 4.05 -0.9x + x2 = 4.05 The x term is -0.9x. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9x + 0.2025 + x2 = 4.05 + 0.2025 Reorder the terms: 0.2025 + -0.9x + x2 = 4.05 + 0.2025 Combine like terms: 4.05 + 0.2025 = 4.2525 0.2025 + -0.9x + x2 = 4.2525 Factor a perfect square on the left side: ((x) + -0.45)((x) + -0.45) = 4.2525 Calculate the square root of the right side: 2.062159063 Break this problem into two subproblems by setting ((x) + -0.45) equal to 2.062159063 and -2.062159063.Subproblem 1
(x) + -0.45 = 2.062159063 Simplifying (x) + -0.45 = 2.062159063 x + -0.45 = 2.062159063 Reorder the terms: -0.45 + x = 2.062159063 Solving -0.45 + x = 2.062159063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = 2.062159063 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = 2.062159063 + 0.45 x = 2.062159063 + 0.45 Combine like terms: 2.062159063 + 0.45 = 2.512159063 x = 2.512159063 Simplifying x = 2.512159063Subproblem 2
(x) + -0.45 = -2.062159063 Simplifying (x) + -0.45 = -2.062159063 x + -0.45 = -2.062159063 Reorder the terms: -0.45 + x = -2.062159063 Solving -0.45 + x = -2.062159063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = -2.062159063 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = -2.062159063 + 0.45 x = -2.062159063 + 0.45 Combine like terms: -2.062159063 + 0.45 = -1.612159063 x = -1.612159063 Simplifying x = -1.612159063Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.512159063, -1.612159063}
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