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Simplifying X2 + 0.2X + -0.024 = 0 Reorder the terms: -0.024 + 0.2X + X2 = 0 Solving -0.024 + 0.2X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '0.024' to each side of the equation. -0.024 + 0.2X + 0.024 + X2 = 0 + 0.024 Reorder the terms: -0.024 + 0.024 + 0.2X + X2 = 0 + 0.024 Combine like terms: -0.024 + 0.024 = 0.000 0.000 + 0.2X + X2 = 0 + 0.024 0.2X + X2 = 0 + 0.024 Combine like terms: 0 + 0.024 = 0.024 0.2X + X2 = 0.024 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 = 0.024 + 0.01 Reorder the terms: 0.01 + 0.2X + X2 = 0.024 + 0.01 Combine like terms: 0.024 + 0.01 = 0.034 0.01 + 0.2X + X2 = 0.034 Factor a perfect square on the left side: (X + 0.1)(X + 0.1) = 0.034 Calculate the square root of the right side: 0.184390889 Break this problem into two subproblems by setting (X + 0.1) equal to 0.184390889 and -0.184390889.Subproblem 1
X + 0.1 = 0.184390889 Simplifying X + 0.1 = 0.184390889 Reorder the terms: 0.1 + X = 0.184390889 Solving 0.1 + X = 0.184390889 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 = 0.184390889 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + X = 0.184390889 + -0.1 X = 0.184390889 + -0.1 Combine like terms: 0.184390889 + -0.1 = 0.084390889 X = 0.084390889 Simplifying X = 0.084390889Subproblem 2
X + 0.1 = -0.184390889 Simplifying X + 0.1 = -0.184390889 Reorder the terms: 0.1 + X = -0.184390889 Solving 0.1 + X = -0.184390889 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 = -0.184390889 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + X = -0.184390889 + -0.1 X = -0.184390889 + -0.1 Combine like terms: -0.184390889 + -0.1 = -0.284390889 X = -0.284390889 Simplifying X = -0.284390889Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.084390889, -0.284390889}
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