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Simplifying 81x2 + 2x + -47 = 0 Reorder the terms: -47 + 2x + 81x2 = 0 Solving -47 + 2x + 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'. -0.5802469136 + 0.02469135802x + x2 = 0 Move the constant term to the right: Add '0.5802469136' to each side of the equation. -0.5802469136 + 0.02469135802x + 0.5802469136 + x2 = 0 + 0.5802469136 Reorder the terms: -0.5802469136 + 0.5802469136 + 0.02469135802x + x2 = 0 + 0.5802469136 Combine like terms: -0.5802469136 + 0.5802469136 = 0.0000000000 0.0000000000 + 0.02469135802x + x2 = 0 + 0.5802469136 0.02469135802x + x2 = 0 + 0.5802469136 Combine like terms: 0 + 0.5802469136 = 0.5802469136 0.02469135802x + x2 = 0.5802469136 The x term is 0.02469135802x. Take half its coefficient (0.01234567901). Square it (0.0001524157902) and add it to both sides. Add '0.0001524157902' to each side of the equation. 0.02469135802x + 0.0001524157902 + x2 = 0.5802469136 + 0.0001524157902 Reorder the terms: 0.0001524157902 + 0.02469135802x + x2 = 0.5802469136 + 0.0001524157902 Combine like terms: 0.5802469136 + 0.0001524157902 = 0.5803993293902 0.0001524157902 + 0.02469135802x + x2 = 0.5803993293902 Factor a perfect square on the left side: (x + 0.01234567901)(x + 0.01234567901) = 0.5803993293902 Calculate the square root of the right side: 0.761839438 Break this problem into two subproblems by setting (x + 0.01234567901) equal to 0.761839438 and -0.761839438.Subproblem 1
x + 0.01234567901 = 0.761839438 Simplifying x + 0.01234567901 = 0.761839438 Reorder the terms: 0.01234567901 + x = 0.761839438 Solving 0.01234567901 + x = 0.761839438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01234567901' to each side of the equation. 0.01234567901 + -0.01234567901 + x = 0.761839438 + -0.01234567901 Combine like terms: 0.01234567901 + -0.01234567901 = 0.00000000000 0.00000000000 + x = 0.761839438 + -0.01234567901 x = 0.761839438 + -0.01234567901 Combine like terms: 0.761839438 + -0.01234567901 = 0.74949375899 x = 0.74949375899 Simplifying x = 0.74949375899Subproblem 2
x + 0.01234567901 = -0.761839438 Simplifying x + 0.01234567901 = -0.761839438 Reorder the terms: 0.01234567901 + x = -0.761839438 Solving 0.01234567901 + x = -0.761839438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01234567901' to each side of the equation. 0.01234567901 + -0.01234567901 + x = -0.761839438 + -0.01234567901 Combine like terms: 0.01234567901 + -0.01234567901 = 0.00000000000 0.00000000000 + x = -0.761839438 + -0.01234567901 x = -0.761839438 + -0.01234567901 Combine like terms: -0.761839438 + -0.01234567901 = -0.77418511701 x = -0.77418511701 Simplifying x = -0.77418511701Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.74949375899, -0.77418511701}
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