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Simplifying x2 + 0.2x = 1 Reorder the terms: 0.2x + x2 = 1 Solving 0.2x + x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 0.2x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 0.2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.2x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.2x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.2x + x2 = 0 + 1 0.2x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.2x + x2 = 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 = 1 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 1 + 0.01 Combine like terms: 1 + 0.01 = 1.01 0.01 + 0.2x + x2 = 1.01 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 1.01 Calculate the square root of the right side: 1.004987562 Break this problem into two subproblems by setting (x + 0.1) equal to 1.004987562 and -1.004987562.Subproblem 1
x + 0.1 = 1.004987562 Simplifying x + 0.1 = 1.004987562 Reorder the terms: 0.1 + x = 1.004987562 Solving 0.1 + x = 1.004987562 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 = 1.004987562 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 1.004987562 + -0.1 x = 1.004987562 + -0.1 Combine like terms: 1.004987562 + -0.1 = 0.904987562 x = 0.904987562 Simplifying x = 0.904987562Subproblem 2
x + 0.1 = -1.004987562 Simplifying x + 0.1 = -1.004987562 Reorder the terms: 0.1 + x = -1.004987562 Solving 0.1 + x = -1.004987562 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 = -1.004987562 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -1.004987562 + -0.1 x = -1.004987562 + -0.1 Combine like terms: -1.004987562 + -0.1 = -1.104987562 x = -1.104987562 Simplifying x = -1.104987562Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.904987562, -1.104987562}
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