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Simplifying x2 + 0.845x + -0.18421 = 0 Reorder the terms: -0.18421 + 0.845x + x2 = 0 Solving -0.18421 + 0.845x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.18421' to each side of the equation. -0.18421 + 0.845x + 0.18421 + x2 = 0 + 0.18421 Reorder the terms: -0.18421 + 0.18421 + 0.845x + x2 = 0 + 0.18421 Combine like terms: -0.18421 + 0.18421 = 0.00000 0.00000 + 0.845x + x2 = 0 + 0.18421 0.845x + x2 = 0 + 0.18421 Combine like terms: 0 + 0.18421 = 0.18421 0.845x + x2 = 0.18421 The x term is 0.845x. Take half its coefficient (0.4225). Square it (0.17850625) and add it to both sides. Add '0.17850625' to each side of the equation. 0.845x + 0.17850625 + x2 = 0.18421 + 0.17850625 Reorder the terms: 0.17850625 + 0.845x + x2 = 0.18421 + 0.17850625 Combine like terms: 0.18421 + 0.17850625 = 0.36271625 0.17850625 + 0.845x + x2 = 0.36271625 Factor a perfect square on the left side: (x + 0.4225)(x + 0.4225) = 0.36271625 Calculate the square root of the right side: 0.602259288 Break this problem into two subproblems by setting (x + 0.4225) equal to 0.602259288 and -0.602259288.Subproblem 1
x + 0.4225 = 0.602259288 Simplifying x + 0.4225 = 0.602259288 Reorder the terms: 0.4225 + x = 0.602259288 Solving 0.4225 + x = 0.602259288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4225' to each side of the equation. 0.4225 + -0.4225 + x = 0.602259288 + -0.4225 Combine like terms: 0.4225 + -0.4225 = 0.0000 0.0000 + x = 0.602259288 + -0.4225 x = 0.602259288 + -0.4225 Combine like terms: 0.602259288 + -0.4225 = 0.179759288 x = 0.179759288 Simplifying x = 0.179759288Subproblem 2
x + 0.4225 = -0.602259288 Simplifying x + 0.4225 = -0.602259288 Reorder the terms: 0.4225 + x = -0.602259288 Solving 0.4225 + x = -0.602259288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4225' to each side of the equation. 0.4225 + -0.4225 + x = -0.602259288 + -0.4225 Combine like terms: 0.4225 + -0.4225 = 0.0000 0.0000 + x = -0.602259288 + -0.4225 x = -0.602259288 + -0.4225 Combine like terms: -0.602259288 + -0.4225 = -1.024759288 x = -1.024759288 Simplifying x = -1.024759288Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.179759288, -1.024759288}
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