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Simplifying (4x2 + -4x + -4x3 + 3) + -1(2x2 + -8x + -4x3 + 4) = 0 Reorder the terms: (3 + -4x + 4x2 + -4x3) + -1(2x2 + -8x + -4x3 + 4) = 0 Remove parenthesis around (3 + -4x + 4x2 + -4x3) 3 + -4x + 4x2 + -4x3 + -1(2x2 + -8x + -4x3 + 4) = 0 Reorder the terms: 3 + -4x + 4x2 + -4x3 + -1(4 + -8x + 2x2 + -4x3) = 0 3 + -4x + 4x2 + -4x3 + (4 * -1 + -8x * -1 + 2x2 * -1 + -4x3 * -1) = 0 3 + -4x + 4x2 + -4x3 + (-4 + 8x + -2x2 + 4x3) = 0 Reorder the terms: 3 + -4 + -4x + 8x + 4x2 + -2x2 + -4x3 + 4x3 = 0 Combine like terms: 3 + -4 = -1 -1 + -4x + 8x + 4x2 + -2x2 + -4x3 + 4x3 = 0 Combine like terms: -4x + 8x = 4x -1 + 4x + 4x2 + -2x2 + -4x3 + 4x3 = 0 Combine like terms: 4x2 + -2x2 = 2x2 -1 + 4x + 2x2 + -4x3 + 4x3 = 0 Combine like terms: -4x3 + 4x3 = 0 -1 + 4x + 2x2 + 0 = 0 -1 + 4x + 2x2 = 0 Solving -1 + 4x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 2x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 2x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 2x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 2x + x2 = 0 + 0.5 2x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 2x + x2 = 0.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.5 + 1 Reorder the terms: 1 + 2x + x2 = 0.5 + 1 Combine like terms: 0.5 + 1 = 1.5 1 + 2x + x2 = 1.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + 1) equal to 1.224744871 and -1.224744871.Subproblem 1
x + 1 = 1.224744871 Simplifying x + 1 = 1.224744871 Reorder the terms: 1 + x = 1.224744871 Solving 1 + x = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.224744871 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.224744871 + -1 x = 1.224744871 + -1 Combine like terms: 1.224744871 + -1 = 0.224744871 x = 0.224744871 Simplifying x = 0.224744871Subproblem 2
x + 1 = -1.224744871 Simplifying x + 1 = -1.224744871 Reorder the terms: 1 + x = -1.224744871 Solving 1 + x = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.224744871 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.224744871 + -1 x = -1.224744871 + -1 Combine like terms: -1.224744871 + -1 = -2.224744871 x = -2.224744871 Simplifying x = -2.224744871Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.224744871, -2.224744871}
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