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Simplifying x + 4 + -9x2 = 0 Reorder the terms: 4 + x + -9x2 = 0 Solving 4 + x + -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'. -0.4444444444 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -0.1111111111x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -0.1111111111x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -0.1111111111x + x2 = 0 + 0.4444444444 -0.1111111111x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -0.1111111111x + x2 = 0.4444444444 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.1111111111x + 0.25 + x2 = 0.4444444444 + 0.25 Reorder the terms: 0.25 + -0.1111111111x + x2 = 0.4444444444 + 0.25 Combine like terms: 0.4444444444 + 0.25 = 0.6944444444 0.25 + -0.1111111111x + x2 = 0.6944444444 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.6944444444 Calculate the square root of the right side: 0.833333333 Break this problem into two subproblems by setting (x + 0.5) equal to 0.833333333 and -0.833333333.Subproblem 1
x + 0.5 = 0.833333333 Simplifying x + 0.5 = 0.833333333 Reorder the terms: 0.5 + x = 0.833333333 Solving 0.5 + x = 0.833333333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.833333333 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.833333333 + -0.5 x = 0.833333333 + -0.5 Combine like terms: 0.833333333 + -0.5 = 0.333333333 x = 0.333333333 Simplifying x = 0.333333333Subproblem 2
x + 0.5 = -0.833333333 Simplifying x + 0.5 = -0.833333333 Reorder the terms: 0.5 + x = -0.833333333 Solving 0.5 + x = -0.833333333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.833333333 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.833333333 + -0.5 x = -0.833333333 + -0.5 Combine like terms: -0.833333333 + -0.5 = -1.333333333 x = -1.333333333 Simplifying x = -1.333333333Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.333333333, -1.333333333}
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