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Simplifying -9x2 + -5x + 1 = 0 Reorder the terms: 1 + -5x + -9x2 = 0 Solving 1 + -5x + -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 + 0.5555555556x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.5555555556x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + 0.5555555556x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + 0.5555555556x + x2 = 0 + 0.1111111111 0.5555555556x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 0.5555555556x + x2 = 0.1111111111 The x term is 0.5555555556x. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556x + 0.07716049384 + x2 = 0.1111111111 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556x + x2 = 0.1111111111 + 0.07716049384 Combine like terms: 0.1111111111 + 0.07716049384 = 0.18827160494 0.07716049384 + 0.5555555556x + x2 = 0.18827160494 Factor a perfect square on the left side: (x + 0.2777777778)(x + 0.2777777778) = 0.18827160494 Calculate the square root of the right side: 0.43390276 Break this problem into two subproblems by setting (x + 0.2777777778) equal to 0.43390276 and -0.43390276.Subproblem 1
x + 0.2777777778 = 0.43390276 Simplifying x + 0.2777777778 = 0.43390276 Reorder the terms: 0.2777777778 + x = 0.43390276 Solving 0.2777777778 + x = 0.43390276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = 0.43390276 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 0.43390276 + -0.2777777778 x = 0.43390276 + -0.2777777778 Combine like terms: 0.43390276 + -0.2777777778 = 0.1561249822 x = 0.1561249822 Simplifying x = 0.1561249822Subproblem 2
x + 0.2777777778 = -0.43390276 Simplifying x + 0.2777777778 = -0.43390276 Reorder the terms: 0.2777777778 + x = -0.43390276 Solving 0.2777777778 + x = -0.43390276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = -0.43390276 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -0.43390276 + -0.2777777778 x = -0.43390276 + -0.2777777778 Combine like terms: -0.43390276 + -0.2777777778 = -0.7116805378 x = -0.7116805378 Simplifying x = -0.7116805378Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1561249822, -0.7116805378}
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