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Simplifying 9x2 + 5x + -2 = 0 Reorder the terms: -2 + 5x + 9x2 = 0 Solving -2 + 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'. -0.2222222222 + 0.5555555556x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.5555555556x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 0.5555555556x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 0.5555555556x + x2 = 0 + 0.2222222222 0.5555555556x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 0.5555555556x + x2 = 0.2222222222 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 = 0.2222222222 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556x + x2 = 0.2222222222 + 0.07716049384 Combine like terms: 0.2222222222 + 0.07716049384 = 0.29938271604 0.07716049384 + 0.5555555556x + x2 = 0.29938271604 Factor a perfect square on the left side: (x + 0.2777777778)(x + 0.2777777778) = 0.29938271604 Calculate the square root of the right side: 0.547158767 Break this problem into two subproblems by setting (x + 0.2777777778) equal to 0.547158767 and -0.547158767.Subproblem 1
x + 0.2777777778 = 0.547158767 Simplifying x + 0.2777777778 = 0.547158767 Reorder the terms: 0.2777777778 + x = 0.547158767 Solving 0.2777777778 + x = 0.547158767 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 = 0.547158767 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 0.547158767 + -0.2777777778 x = 0.547158767 + -0.2777777778 Combine like terms: 0.547158767 + -0.2777777778 = 0.2693809892 x = 0.2693809892 Simplifying x = 0.2693809892Subproblem 2
x + 0.2777777778 = -0.547158767 Simplifying x + 0.2777777778 = -0.547158767 Reorder the terms: 0.2777777778 + x = -0.547158767 Solving 0.2777777778 + x = -0.547158767 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 = -0.547158767 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -0.547158767 + -0.2777777778 x = -0.547158767 + -0.2777777778 Combine like terms: -0.547158767 + -0.2777777778 = -0.8249365448 x = -0.8249365448 Simplifying x = -0.8249365448Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2693809892, -0.8249365448}
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