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Simplifying 81x2 + 36x + 2 = 0 Reorder the terms: 2 + 36x + 81x2 = 0 Solving 2 + 36x + 81x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. 0.02469135802 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '-0.02469135802' to each side of the equation. 0.02469135802 + 0.4444444444x + -0.02469135802 + x2 = 0 + -0.02469135802 Reorder the terms: 0.02469135802 + -0.02469135802 + 0.4444444444x + x2 = 0 + -0.02469135802 Combine like terms: 0.02469135802 + -0.02469135802 = 0.00000000000 0.00000000000 + 0.4444444444x + x2 = 0 + -0.02469135802 0.4444444444x + x2 = 0 + -0.02469135802 Combine like terms: 0 + -0.02469135802 = -0.02469135802 0.4444444444x + x2 = -0.02469135802 The x term is 0.4444444444x. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x + 0.04938271604 + x2 = -0.02469135802 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = -0.02469135802 + 0.04938271604 Combine like terms: -0.02469135802 + 0.04938271604 = 0.02469135802 0.04938271604 + 0.4444444444x + x2 = 0.02469135802 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 0.02469135802 Calculate the square root of the right side: 0.15713484 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 0.15713484 and -0.15713484.Subproblem 1
x + 0.2222222222 = 0.15713484 Simplifying x + 0.2222222222 = 0.15713484 Reorder the terms: 0.2222222222 + x = 0.15713484 Solving 0.2222222222 + x = 0.15713484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = 0.15713484 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 0.15713484 + -0.2222222222 x = 0.15713484 + -0.2222222222 Combine like terms: 0.15713484 + -0.2222222222 = -0.0650873822 x = -0.0650873822 Simplifying x = -0.0650873822Subproblem 2
x + 0.2222222222 = -0.15713484 Simplifying x + 0.2222222222 = -0.15713484 Reorder the terms: 0.2222222222 + x = -0.15713484 Solving 0.2222222222 + x = -0.15713484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = -0.15713484 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -0.15713484 + -0.2222222222 x = -0.15713484 + -0.2222222222 Combine like terms: -0.15713484 + -0.2222222222 = -0.3793570622 x = -0.3793570622 Simplifying x = -0.3793570622Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0650873822, -0.3793570622}
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