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Simplifying 2x + x2 = 0.01 Solving 2x + x2 = 0.01 Solving for variable 'x'. Reorder the terms: -0.01 + 2x + x2 = 0.01 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 -0.01 + 2x + x2 = 0.00 Begin completing the square. 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 = 1.01 1 + 2x + x2 = 1.01 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.01 Calculate the square root of the right side: 1.004987562 Break this problem into two subproblems by setting (x + 1) equal to 1.004987562 and -1.004987562.Subproblem 1
x + 1 = 1.004987562 Simplifying x + 1 = 1.004987562 Reorder the terms: 1 + x = 1.004987562 Solving 1 + x = 1.004987562 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 = 1.004987562 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.004987562 + -1 x = 1.004987562 + -1 Combine like terms: 1.004987562 + -1 = 0.004987562 x = 0.004987562 Simplifying x = 0.004987562Subproblem 2
x + 1 = -1.004987562 Simplifying x + 1 = -1.004987562 Reorder the terms: 1 + x = -1.004987562 Solving 1 + x = -1.004987562 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 = -1.004987562 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.004987562 + -1 x = -1.004987562 + -1 Combine like terms: -1.004987562 + -1 = -2.004987562 x = -2.004987562 Simplifying x = -2.004987562Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.004987562, -2.004987562}
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