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Simplifying 9x2 + 10x + -9 = 0 Reorder the terms: -9 + 10x + 9x2 = 0 Solving -9 + 10x + 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'. -1 + 1.111111111x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.111111111x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 1.111111111x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.111111111x + x2 = 0 + 1 1.111111111x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.111111111x + x2 = 1 The x term is 1.111111111x. Take half its coefficient (0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. 1.111111111x + 0.3086419752 + x2 = 1 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111x + x2 = 1 + 0.3086419752 Combine like terms: 1 + 0.3086419752 = 1.3086419752 0.3086419752 + 1.111111111x + x2 = 1.3086419752 Factor a perfect square on the left side: (x + 0.5555555555)(x + 0.5555555555) = 1.3086419752 Calculate the square root of the right side: 1.143958905 Break this problem into two subproblems by setting (x + 0.5555555555) equal to 1.143958905 and -1.143958905.Subproblem 1
x + 0.5555555555 = 1.143958905 Simplifying x + 0.5555555555 = 1.143958905 Reorder the terms: 0.5555555555 + x = 1.143958905 Solving 0.5555555555 + x = 1.143958905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = 1.143958905 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = 1.143958905 + -0.5555555555 x = 1.143958905 + -0.5555555555 Combine like terms: 1.143958905 + -0.5555555555 = 0.5884033495 x = 0.5884033495 Simplifying x = 0.5884033495Subproblem 2
x + 0.5555555555 = -1.143958905 Simplifying x + 0.5555555555 = -1.143958905 Reorder the terms: 0.5555555555 + x = -1.143958905 Solving 0.5555555555 + x = -1.143958905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = -1.143958905 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = -1.143958905 + -0.5555555555 x = -1.143958905 + -0.5555555555 Combine like terms: -1.143958905 + -0.5555555555 = -1.6995144605 x = -1.6995144605 Simplifying x = -1.6995144605Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5884033495, -1.6995144605}
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