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Simplifying 2x + -1x2 = 0.01 Solving 2x + -1x2 = 0.01 Solving for variable 'x'. Reorder the terms: -0.01 + 2x + -1x2 = 0.01 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 -0.01 + 2x + -1x2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.01 + -2x + x2 = 0.00 Move the constant term to the right: Add '-0.01' to each side of the equation. 0.01 + -2x + -0.01 + x2 = 0.00 + -0.01 Reorder the terms: 0.01 + -0.01 + -2x + x2 = 0.00 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + -2x + x2 = 0.00 + -0.01 -2x + x2 = 0.00 + -0.01 Combine like terms: 0.00 + -0.01 = -0.01 -2x + x2 = -0.01 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.01 + 1 Reorder the terms: 1 + -2x + x2 = -0.01 + 1 Combine like terms: -0.01 + 1 = 0.99 1 + -2x + x2 = 0.99 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.99 Calculate the square root of the right side: 0.994987437 Break this problem into two subproblems by setting (x + -1) equal to 0.994987437 and -0.994987437.Subproblem 1
x + -1 = 0.994987437 Simplifying x + -1 = 0.994987437 Reorder the terms: -1 + x = 0.994987437 Solving -1 + x = 0.994987437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.994987437 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.994987437 + 1 x = 0.994987437 + 1 Combine like terms: 0.994987437 + 1 = 1.994987437 x = 1.994987437 Simplifying x = 1.994987437Subproblem 2
x + -1 = -0.994987437 Simplifying x + -1 = -0.994987437 Reorder the terms: -1 + x = -0.994987437 Solving -1 + x = -0.994987437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.994987437 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.994987437 + 1 x = -0.994987437 + 1 Combine like terms: -0.994987437 + 1 = 0.005012563 x = 0.005012563 Simplifying x = 0.005012563Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.994987437, 0.005012563}
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