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Simplifying x2 + -0.4x + -2 = 0 Reorder the terms: -2 + -0.4x + x2 = 0 Solving -2 + -0.4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.4x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.4x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.4x + x2 = 0 + 2 -0.4x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.4x + x2 = 2 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 = 2 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 2 + 0.04 Combine like terms: 2 + 0.04 = 2.04 0.04 + -0.4x + x2 = 2.04 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 2.04 Calculate the square root of the right side: 1.428285686 Break this problem into two subproblems by setting (x + -0.2) equal to 1.428285686 and -1.428285686.Subproblem 1
x + -0.2 = 1.428285686 Simplifying x + -0.2 = 1.428285686 Reorder the terms: -0.2 + x = 1.428285686 Solving -0.2 + x = 1.428285686 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 = 1.428285686 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.428285686 + 0.2 x = 1.428285686 + 0.2 Combine like terms: 1.428285686 + 0.2 = 1.628285686 x = 1.628285686 Simplifying x = 1.628285686Subproblem 2
x + -0.2 = -1.428285686 Simplifying x + -0.2 = -1.428285686 Reorder the terms: -0.2 + x = -1.428285686 Solving -0.2 + x = -1.428285686 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 = -1.428285686 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.428285686 + 0.2 x = -1.428285686 + 0.2 Combine like terms: -1.428285686 + 0.2 = -1.228285686 x = -1.228285686 Simplifying x = -1.228285686Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.628285686, -1.228285686}
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