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Simplifying 25x2 + 45x + -11 = 0 Reorder the terms: -11 + 45x + 25x2 = 0 Solving -11 + 45x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.44 + 1.8x + x2 = 0 Move the constant term to the right: Add '0.44' to each side of the equation. -0.44 + 1.8x + 0.44 + x2 = 0 + 0.44 Reorder the terms: -0.44 + 0.44 + 1.8x + x2 = 0 + 0.44 Combine like terms: -0.44 + 0.44 = 0.00 0.00 + 1.8x + x2 = 0 + 0.44 1.8x + x2 = 0 + 0.44 Combine like terms: 0 + 0.44 = 0.44 1.8x + x2 = 0.44 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 0.44 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 0.44 + 0.81 Combine like terms: 0.44 + 0.81 = 1.25 0.81 + 1.8x + x2 = 1.25 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 0.9) equal to 1.118033989 and -1.118033989.Subproblem 1
x + 0.9 = 1.118033989 Simplifying x + 0.9 = 1.118033989 Reorder the terms: 0.9 + x = 1.118033989 Solving 0.9 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 1.118033989 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 1.118033989 + -0.9 x = 1.118033989 + -0.9 Combine like terms: 1.118033989 + -0.9 = 0.218033989 x = 0.218033989 Simplifying x = 0.218033989Subproblem 2
x + 0.9 = -1.118033989 Simplifying x + 0.9 = -1.118033989 Reorder the terms: 0.9 + x = -1.118033989 Solving 0.9 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -1.118033989 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -1.118033989 + -0.9 x = -1.118033989 + -0.9 Combine like terms: -1.118033989 + -0.9 = -2.018033989 x = -2.018033989 Simplifying x = -2.018033989Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.218033989, -2.018033989}
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