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Simplifying 2x2 = 0.4x + 0.2 Reorder the terms: 2x2 = 0.2 + 0.4x Solving 2x2 = 0.2 + 0.4x Solving for variable 'x'. Reorder the terms: -0.2 + -0.4x + 2x2 = 0.2 + 0.4x + -0.2 + -0.4x Reorder the terms: -0.2 + -0.4x + 2x2 = 0.2 + -0.2 + 0.4x + -0.4x Combine like terms: 0.2 + -0.2 = 0.0 -0.2 + -0.4x + 2x2 = 0.0 + 0.4x + -0.4x -0.2 + -0.4x + 2x2 = 0.4x + -0.4x Combine like terms: 0.4x + -0.4x = 0.0 -0.2 + -0.4x + 2x2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.1 + -0.2x + x2 = 0.0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -0.2x + 0.1 + x2 = 0.0 + 0.1 Reorder the terms: -0.1 + 0.1 + -0.2x + x2 = 0.0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -0.2x + x2 = 0.0 + 0.1 -0.2x + x2 = 0.0 + 0.1 Combine like terms: 0.0 + 0.1 = 0.1 -0.2x + x2 = 0.1 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 = 0.1 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 0.1 + 0.01 Combine like terms: 0.1 + 0.01 = 0.11 0.01 + -0.2x + x2 = 0.11 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 0.11 Calculate the square root of the right side: 0.331662479 Break this problem into two subproblems by setting (x + -0.1) equal to 0.331662479 and -0.331662479.Subproblem 1
x + -0.1 = 0.331662479 Simplifying x + -0.1 = 0.331662479 Reorder the terms: -0.1 + x = 0.331662479 Solving -0.1 + x = 0.331662479 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 = 0.331662479 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 0.331662479 + 0.1 x = 0.331662479 + 0.1 Combine like terms: 0.331662479 + 0.1 = 0.431662479 x = 0.431662479 Simplifying x = 0.431662479Subproblem 2
x + -0.1 = -0.331662479 Simplifying x + -0.1 = -0.331662479 Reorder the terms: -0.1 + x = -0.331662479 Solving -0.1 + x = -0.331662479 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 = -0.331662479 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -0.331662479 + 0.1 x = -0.331662479 + 0.1 Combine like terms: -0.331662479 + 0.1 = -0.231662479 x = -0.231662479 Simplifying x = -0.231662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.431662479, -0.231662479}
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