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Simplifying 3x + -5x + 9x2 + -5 = 0 Reorder the terms: -5 + 3x + -5x + 9x2 = 0 Combine like terms: 3x + -5x = -2x -5 + -2x + 9x2 = 0 Solving -5 + -2x + 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'. -0.5555555556 + -0.2222222222x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -0.2222222222x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -0.2222222222x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -0.2222222222x + x2 = 0 + 0.5555555556 -0.2222222222x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -0.2222222222x + x2 = 0.5555555556 The x term is -0.2222222222x. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222x + 0.01234567901 + x2 = 0.5555555556 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x + x2 = 0.5555555556 + 0.01234567901 Combine like terms: 0.5555555556 + 0.01234567901 = 0.56790123461 0.01234567901 + -0.2222222222x + x2 = 0.56790123461 Factor a perfect square on the left side: (x + -0.1111111111)(x + -0.1111111111) = 0.56790123461 Calculate the square root of the right side: 0.75359222 Break this problem into two subproblems by setting (x + -0.1111111111) equal to 0.75359222 and -0.75359222.Subproblem 1
x + -0.1111111111 = 0.75359222 Simplifying x + -0.1111111111 = 0.75359222 Reorder the terms: -0.1111111111 + x = 0.75359222 Solving -0.1111111111 + x = 0.75359222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = 0.75359222 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = 0.75359222 + 0.1111111111 x = 0.75359222 + 0.1111111111 Combine like terms: 0.75359222 + 0.1111111111 = 0.8647033311 x = 0.8647033311 Simplifying x = 0.8647033311Subproblem 2
x + -0.1111111111 = -0.75359222 Simplifying x + -0.1111111111 = -0.75359222 Reorder the terms: -0.1111111111 + x = -0.75359222 Solving -0.1111111111 + x = -0.75359222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = -0.75359222 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = -0.75359222 + 0.1111111111 x = -0.75359222 + 0.1111111111 Combine like terms: -0.75359222 + 0.1111111111 = -0.6424811089 x = -0.6424811089 Simplifying x = -0.6424811089Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8647033311, -0.6424811089}
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