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Simplifying (9x2) + (8x) + 1 = 0 Reorder the terms: 1 + (8x) + (9x2) = 0 Solving 1 + (8x) + (9x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + (0.8888888889x) + x2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + (0.8888888889x) + -0.1111111111 + x2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + (0.8888888889x) + x2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + (0.8888888889x) + x2 = 0 + -0.1111111111 (0.8888888889x) + x2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 (0.8888888889x) + x2 = -0.1111111111 The x term is (0.8888888889x). Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. (0.8888888889x) + 0.1975308642 + x2 = -0.1111111111 + 0.1975308642 Reorder the terms: 0.1975308642 + (0.8888888889x) + x2 = -0.1111111111 + 0.1975308642 Combine like terms: -0.1111111111 + 0.1975308642 = 0.0864197531 0.1975308642 + (0.8888888889x) + x2 = 0.0864197531 Factor a perfect square on the left side: ((x) + 0.4444444445)((x) + 0.4444444445) = 0.0864197531 Calculate the square root of the right side: 0.293972368 Break this problem into two subproblems by setting ((x) + 0.4444444445) equal to 0.293972368 and -0.293972368.Subproblem 1
(x) + 0.4444444445 = 0.293972368 Simplifying (x) + 0.4444444445 = 0.293972368 x + 0.4444444445 = 0.293972368 Reorder the terms: 0.4444444445 + x = 0.293972368 Solving 0.4444444445 + x = 0.293972368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = 0.293972368 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = 0.293972368 + -0.4444444445 x = 0.293972368 + -0.4444444445 Combine like terms: 0.293972368 + -0.4444444445 = -0.1504720765 x = -0.1504720765 Simplifying x = -0.1504720765Subproblem 2
(x) + 0.4444444445 = -0.293972368 Simplifying (x) + 0.4444444445 = -0.293972368 x + 0.4444444445 = -0.293972368 Reorder the terms: 0.4444444445 + x = -0.293972368 Solving 0.4444444445 + x = -0.293972368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = -0.293972368 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = -0.293972368 + -0.4444444445 x = -0.293972368 + -0.4444444445 Combine like terms: -0.293972368 + -0.4444444445 = -0.7384168125 x = -0.7384168125 Simplifying x = -0.7384168125Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1504720765, -0.7384168125}
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