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Simplifying x2 + 0.2x + -0.065 = 0 Reorder the terms: -0.065 + 0.2x + x2 = 0 Solving -0.065 + 0.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.065' to each side of the equation. -0.065 + 0.2x + 0.065 + x2 = 0 + 0.065 Reorder the terms: -0.065 + 0.065 + 0.2x + x2 = 0 + 0.065 Combine like terms: -0.065 + 0.065 = 0.000 0.000 + 0.2x + x2 = 0 + 0.065 0.2x + x2 = 0 + 0.065 Combine like terms: 0 + 0.065 = 0.065 0.2x + x2 = 0.065 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 = 0.065 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.065 + 0.01 Combine like terms: 0.065 + 0.01 = 0.075 0.01 + 0.2x + x2 = 0.075 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.075 Calculate the square root of the right side: 0.273861279 Break this problem into two subproblems by setting (x + 0.1) equal to 0.273861279 and -0.273861279.Subproblem 1
x + 0.1 = 0.273861279 Simplifying x + 0.1 = 0.273861279 Reorder the terms: 0.1 + x = 0.273861279 Solving 0.1 + x = 0.273861279 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 = 0.273861279 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.273861279 + -0.1 x = 0.273861279 + -0.1 Combine like terms: 0.273861279 + -0.1 = 0.173861279 x = 0.173861279 Simplifying x = 0.173861279Subproblem 2
x + 0.1 = -0.273861279 Simplifying x + 0.1 = -0.273861279 Reorder the terms: 0.1 + x = -0.273861279 Solving 0.1 + x = -0.273861279 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 = -0.273861279 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.273861279 + -0.1 x = -0.273861279 + -0.1 Combine like terms: -0.273861279 + -0.1 = -0.373861279 x = -0.373861279 Simplifying x = -0.373861279Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.173861279, -0.373861279}
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