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Simplifying 4x2 + -81x + 25 = 0 Reorder the terms: 25 + -81x + 4x2 = 0 Solving 25 + -81x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.25 + -20.25x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + -20.25x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + -20.25x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + -20.25x + x2 = 0 + -6.25 -20.25x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 -20.25x + x2 = -6.25 The x term is -20.25x. Take half its coefficient (-10.125). Square it (102.515625) and add it to both sides. Add '102.515625' to each side of the equation. -20.25x + 102.515625 + x2 = -6.25 + 102.515625 Reorder the terms: 102.515625 + -20.25x + x2 = -6.25 + 102.515625 Combine like terms: -6.25 + 102.515625 = 96.265625 102.515625 + -20.25x + x2 = 96.265625 Factor a perfect square on the left side: (x + -10.125)(x + -10.125) = 96.265625 Calculate the square root of the right side: 9.811504727 Break this problem into two subproblems by setting (x + -10.125) equal to 9.811504727 and -9.811504727.Subproblem 1
x + -10.125 = 9.811504727 Simplifying x + -10.125 = 9.811504727 Reorder the terms: -10.125 + x = 9.811504727 Solving -10.125 + x = 9.811504727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.125' to each side of the equation. -10.125 + 10.125 + x = 9.811504727 + 10.125 Combine like terms: -10.125 + 10.125 = 0.000 0.000 + x = 9.811504727 + 10.125 x = 9.811504727 + 10.125 Combine like terms: 9.811504727 + 10.125 = 19.936504727 x = 19.936504727 Simplifying x = 19.936504727Subproblem 2
x + -10.125 = -9.811504727 Simplifying x + -10.125 = -9.811504727 Reorder the terms: -10.125 + x = -9.811504727 Solving -10.125 + x = -9.811504727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.125' to each side of the equation. -10.125 + 10.125 + x = -9.811504727 + 10.125 Combine like terms: -10.125 + 10.125 = 0.000 0.000 + x = -9.811504727 + 10.125 x = -9.811504727 + 10.125 Combine like terms: -9.811504727 + 10.125 = 0.313495273 x = 0.313495273 Simplifying x = 0.313495273Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.936504727, 0.313495273}
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