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Simplifying 0.25x2 + -0.05x + -0.9 = 0 Reorder the terms: -0.9 + -0.05x + 0.25x2 = 0 Solving -0.9 + -0.05x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -3.6 + -0.2x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + -0.2x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + -0.2x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + -0.2x + x2 = 0 + 3.6 -0.2x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 -0.2x + x2 = 3.6 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 3.6 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 3.6 + 0.01 Combine like terms: 3.6 + 0.01 = 3.61 0.01 + -0.2x + x2 = 3.61 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 3.61 Calculate the square root of the right side: 1.9 Break this problem into two subproblems by setting (x + -0.1) equal to 1.9 and -1.9.Subproblem 1
x + -0.1 = 1.9 Simplifying x + -0.1 = 1.9 Reorder the terms: -0.1 + x = 1.9 Solving -0.1 + x = 1.9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 1.9 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 1.9 + 0.1 x = 1.9 + 0.1 Combine like terms: 1.9 + 0.1 = 2 x = 2 Simplifying x = 2Subproblem 2
x + -0.1 = -1.9 Simplifying x + -0.1 = -1.9 Reorder the terms: -0.1 + x = -1.9 Solving -0.1 + x = -1.9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -1.9 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -1.9 + 0.1 x = -1.9 + 0.1 Combine like terms: -1.9 + 0.1 = -1.8 x = -1.8 Simplifying x = -1.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -1.8}
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