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Simplifying x2 + -0.2x + 0.01 = 2x2 Reorder the terms: 0.01 + -0.2x + x2 = 2x2 Solving 0.01 + -0.2x + x2 = 2x2 Solving for variable 'x'. Combine like terms: x2 + -2x2 = -1x2 0.01 + -0.2x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 0.01 + -0.2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.01 + 0.2x + x2 = 0 Move the constant term to the right: Add '0.01' to each side of the equation. -0.01 + 0.2x + 0.01 + x2 = 0 + 0.01 Reorder the terms: -0.01 + 0.01 + 0.2x + x2 = 0 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + 0.2x + x2 = 0 + 0.01 0.2x + x2 = 0 + 0.01 Combine like terms: 0 + 0.01 = 0.01 0.2x + x2 = 0.01 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 = 0.01 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.01 + 0.01 Combine like terms: 0.01 + 0.01 = 0.02 0.01 + 0.2x + x2 = 0.02 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.02 Calculate the square root of the right side: 0.141421356 Break this problem into two subproblems by setting (x + 0.1) equal to 0.141421356 and -0.141421356.Subproblem 1
x + 0.1 = 0.141421356 Simplifying x + 0.1 = 0.141421356 Reorder the terms: 0.1 + x = 0.141421356 Solving 0.1 + x = 0.141421356 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 = 0.141421356 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.141421356 + -0.1 x = 0.141421356 + -0.1 Combine like terms: 0.141421356 + -0.1 = 0.041421356 x = 0.041421356 Simplifying x = 0.041421356Subproblem 2
x + 0.1 = -0.141421356 Simplifying x + 0.1 = -0.141421356 Reorder the terms: 0.1 + x = -0.141421356 Solving 0.1 + x = -0.141421356 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 = -0.141421356 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.141421356 + -0.1 x = -0.141421356 + -0.1 Combine like terms: -0.141421356 + -0.1 = -0.241421356 x = -0.241421356 Simplifying x = -0.241421356Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.041421356, -0.241421356}
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