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Simplifying x2 + -4x + 4 = 0.333 Reorder the terms: 4 + -4x + x2 = 0.333 Solving 4 + -4x + x2 = 0.333 Solving for variable 'x'. Reorder the terms: 4 + -0.333 + -4x + x2 = 0.333 + -0.333 Combine like terms: 4 + -0.333 = 3.667 3.667 + -4x + x2 = 0.333 + -0.333 Combine like terms: 0.333 + -0.333 = 0.000 3.667 + -4x + x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '-3.667' to each side of the equation. 3.667 + -4x + -3.667 + x2 = 0.000 + -3.667 Reorder the terms: 3.667 + -3.667 + -4x + x2 = 0.000 + -3.667 Combine like terms: 3.667 + -3.667 = 0.000 0.000 + -4x + x2 = 0.000 + -3.667 -4x + x2 = 0.000 + -3.667 Combine like terms: 0.000 + -3.667 = -3.667 -4x + x2 = -3.667 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -3.667 + 4 Reorder the terms: 4 + -4x + x2 = -3.667 + 4 Combine like terms: -3.667 + 4 = 0.333 4 + -4x + x2 = 0.333 Factor a perfect square on the left side: (x + -2)(x + -2) = 0.333 Calculate the square root of the right side: 0.577061522 Break this problem into two subproblems by setting (x + -2) equal to 0.577061522 and -0.577061522.Subproblem 1
x + -2 = 0.577061522 Simplifying x + -2 = 0.577061522 Reorder the terms: -2 + x = 0.577061522 Solving -2 + x = 0.577061522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0.577061522 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.577061522 + 2 x = 0.577061522 + 2 Combine like terms: 0.577061522 + 2 = 2.577061522 x = 2.577061522 Simplifying x = 2.577061522Subproblem 2
x + -2 = -0.577061522 Simplifying x + -2 = -0.577061522 Reorder the terms: -2 + x = -0.577061522 Solving -2 + x = -0.577061522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -0.577061522 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.577061522 + 2 x = -0.577061522 + 2 Combine like terms: -0.577061522 + 2 = 1.422938478 x = 1.422938478 Simplifying x = 1.422938478Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.577061522, 1.422938478}
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