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Simplifying 2x2 + 82x + 81 = 0 Reorder the terms: 81 + 82x + 2x2 = 0 Solving 81 + 82x + 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 + 41x + x2 = 0 Move the constant term to the right: Add '-40.5' to each side of the equation. 40.5 + 41x + -40.5 + x2 = 0 + -40.5 Reorder the terms: 40.5 + -40.5 + 41x + x2 = 0 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + 41x + x2 = 0 + -40.5 41x + x2 = 0 + -40.5 Combine like terms: 0 + -40.5 = -40.5 41x + x2 = -40.5 The x term is 41x. Take half its coefficient (20.5). Square it (420.25) and add it to both sides. Add '420.25' to each side of the equation. 41x + 420.25 + x2 = -40.5 + 420.25 Reorder the terms: 420.25 + 41x + x2 = -40.5 + 420.25 Combine like terms: -40.5 + 420.25 = 379.75 420.25 + 41x + x2 = 379.75 Factor a perfect square on the left side: (x + 20.5)(x + 20.5) = 379.75 Calculate the square root of the right side: 19.48717527 Break this problem into two subproblems by setting (x + 20.5) equal to 19.48717527 and -19.48717527.Subproblem 1
x + 20.5 = 19.48717527 Simplifying x + 20.5 = 19.48717527 Reorder the terms: 20.5 + x = 19.48717527 Solving 20.5 + x = 19.48717527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.5' to each side of the equation. 20.5 + -20.5 + x = 19.48717527 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = 19.48717527 + -20.5 x = 19.48717527 + -20.5 Combine like terms: 19.48717527 + -20.5 = -1.01282473 x = -1.01282473 Simplifying x = -1.01282473Subproblem 2
x + 20.5 = -19.48717527 Simplifying x + 20.5 = -19.48717527 Reorder the terms: 20.5 + x = -19.48717527 Solving 20.5 + x = -19.48717527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.5' to each side of the equation. 20.5 + -20.5 + x = -19.48717527 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = -19.48717527 + -20.5 x = -19.48717527 + -20.5 Combine like terms: -19.48717527 + -20.5 = -39.98717527 x = -39.98717527 Simplifying x = -39.98717527Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.01282473, -39.98717527}
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