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Simplifying x2 + 0.4x + -0.09 = 0 Reorder the terms: -0.09 + 0.4x + x2 = 0 Solving -0.09 + 0.4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.09' to each side of the equation. -0.09 + 0.4x + 0.09 + x2 = 0 + 0.09 Reorder the terms: -0.09 + 0.09 + 0.4x + x2 = 0 + 0.09 Combine like terms: -0.09 + 0.09 = 0.00 0.00 + 0.4x + x2 = 0 + 0.09 0.4x + x2 = 0 + 0.09 Combine like terms: 0 + 0.09 = 0.09 0.4x + x2 = 0.09 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.09 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.09 + 0.04 Combine like terms: 0.09 + 0.04 = 0.13 0.04 + 0.4x + x2 = 0.13 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.13 Calculate the square root of the right side: 0.360555128 Break this problem into two subproblems by setting (x + 0.2) equal to 0.360555128 and -0.360555128.Subproblem 1
x + 0.2 = 0.360555128 Simplifying x + 0.2 = 0.360555128 Reorder the terms: 0.2 + x = 0.360555128 Solving 0.2 + x = 0.360555128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.360555128 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.360555128 + -0.2 x = 0.360555128 + -0.2 Combine like terms: 0.360555128 + -0.2 = 0.160555128 x = 0.160555128 Simplifying x = 0.160555128Subproblem 2
x + 0.2 = -0.360555128 Simplifying x + 0.2 = -0.360555128 Reorder the terms: 0.2 + x = -0.360555128 Solving 0.2 + x = -0.360555128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.360555128 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.360555128 + -0.2 x = -0.360555128 + -0.2 Combine like terms: -0.360555128 + -0.2 = -0.560555128 x = -0.560555128 Simplifying x = -0.560555128Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.160555128, -0.560555128}
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