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Simplifying 45x2 + 18x + -40 = 0 Reorder the terms: -40 + 18x + 45x2 = 0 Solving -40 + 18x + 45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.8888888889 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + 0.4x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + 0.4x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + 0.4x + x2 = 0 + 0.8888888889 0.4x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 0.4x + x2 = 0.8888888889 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.8888888889 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.8888888889 + 0.04 Combine like terms: 0.8888888889 + 0.04 = 0.9288888889 0.04 + 0.4x + x2 = 0.9288888889 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.9288888889 Calculate the square root of the right side: 0.96378882 Break this problem into two subproblems by setting (x + 0.2) equal to 0.96378882 and -0.96378882.Subproblem 1
x + 0.2 = 0.96378882 Simplifying x + 0.2 = 0.96378882 Reorder the terms: 0.2 + x = 0.96378882 Solving 0.2 + x = 0.96378882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.96378882 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.96378882 + -0.2 x = 0.96378882 + -0.2 Combine like terms: 0.96378882 + -0.2 = 0.76378882 x = 0.76378882 Simplifying x = 0.76378882Subproblem 2
x + 0.2 = -0.96378882 Simplifying x + 0.2 = -0.96378882 Reorder the terms: 0.2 + x = -0.96378882 Solving 0.2 + x = -0.96378882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.96378882 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.96378882 + -0.2 x = -0.96378882 + -0.2 Combine like terms: -0.96378882 + -0.2 = -1.16378882 x = -1.16378882 Simplifying x = -1.16378882Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.76378882, -1.16378882}
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