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Simplifying 20x2 + 12x + -9 = 0 Reorder the terms: -9 + 12x + 20x2 = 0 Solving -9 + 12x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.45 + 0.6x + x2 = 0 Move the constant term to the right: Add '0.45' to each side of the equation. -0.45 + 0.6x + 0.45 + x2 = 0 + 0.45 Reorder the terms: -0.45 + 0.45 + 0.6x + x2 = 0 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + 0.6x + x2 = 0 + 0.45 0.6x + x2 = 0 + 0.45 Combine like terms: 0 + 0.45 = 0.45 0.6x + x2 = 0.45 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 0.45 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 0.45 + 0.09 Combine like terms: 0.45 + 0.09 = 0.54 0.09 + 0.6x + x2 = 0.54 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 0.54 Calculate the square root of the right side: 0.734846923 Break this problem into two subproblems by setting (x + 0.3) equal to 0.734846923 and -0.734846923.Subproblem 1
x + 0.3 = 0.734846923 Simplifying x + 0.3 = 0.734846923 Reorder the terms: 0.3 + x = 0.734846923 Solving 0.3 + x = 0.734846923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 0.734846923 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 0.734846923 + -0.3 x = 0.734846923 + -0.3 Combine like terms: 0.734846923 + -0.3 = 0.434846923 x = 0.434846923 Simplifying x = 0.434846923Subproblem 2
x + 0.3 = -0.734846923 Simplifying x + 0.3 = -0.734846923 Reorder the terms: 0.3 + x = -0.734846923 Solving 0.3 + x = -0.734846923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -0.734846923 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -0.734846923 + -0.3 x = -0.734846923 + -0.3 Combine like terms: -0.734846923 + -0.3 = -1.034846923 x = -1.034846923 Simplifying x = -1.034846923Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.434846923, -1.034846923}
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