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Simplifying 2x2 + -81x + -21 = 0 Reorder the terms: -21 + -81x + 2x2 = 0 Solving -21 + -81x + 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'. -10.5 + -40.5x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -40.5x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -40.5x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -40.5x + x2 = 0 + 10.5 -40.5x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -40.5x + x2 = 10.5 The x term is -40.5x. Take half its coefficient (-20.25). Square it (410.0625) and add it to both sides. Add '410.0625' to each side of the equation. -40.5x + 410.0625 + x2 = 10.5 + 410.0625 Reorder the terms: 410.0625 + -40.5x + x2 = 10.5 + 410.0625 Combine like terms: 10.5 + 410.0625 = 420.5625 410.0625 + -40.5x + x2 = 420.5625 Factor a perfect square on the left side: (x + -20.25)(x + -20.25) = 420.5625 Calculate the square root of the right side: 20.507620535 Break this problem into two subproblems by setting (x + -20.25) equal to 20.507620535 and -20.507620535.Subproblem 1
x + -20.25 = 20.507620535 Simplifying x + -20.25 = 20.507620535 Reorder the terms: -20.25 + x = 20.507620535 Solving -20.25 + x = 20.507620535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.25' to each side of the equation. -20.25 + 20.25 + x = 20.507620535 + 20.25 Combine like terms: -20.25 + 20.25 = 0.00 0.00 + x = 20.507620535 + 20.25 x = 20.507620535 + 20.25 Combine like terms: 20.507620535 + 20.25 = 40.757620535 x = 40.757620535 Simplifying x = 40.757620535Subproblem 2
x + -20.25 = -20.507620535 Simplifying x + -20.25 = -20.507620535 Reorder the terms: -20.25 + x = -20.507620535 Solving -20.25 + x = -20.507620535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.25' to each side of the equation. -20.25 + 20.25 + x = -20.507620535 + 20.25 Combine like terms: -20.25 + 20.25 = 0.00 0.00 + x = -20.507620535 + 20.25 x = -20.507620535 + 20.25 Combine like terms: -20.507620535 + 20.25 = -0.257620535 x = -0.257620535 Simplifying x = -0.257620535Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.757620535, -0.257620535}
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