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Simplifying (1 + -2x)(1 + -2x) = 2.4x Multiply (1 + -2x) * (1 + -2x) (1(1 + -2x) + -2x * (1 + -2x)) = 2.4x ((1 * 1 + -2x * 1) + -2x * (1 + -2x)) = 2.4x ((1 + -2x) + -2x * (1 + -2x)) = 2.4x (1 + -2x + (1 * -2x + -2x * -2x)) = 2.4x (1 + -2x + (-2x + 4x2)) = 2.4x Combine like terms: -2x + -2x = -4x (1 + -4x + 4x2) = 2.4x Solving 1 + -4x + 4x2 = 2.4x Solving for variable 'x'. Reorder the terms: 1 + -4x + -2.4x + 4x2 = 2.4x + -2.4x Combine like terms: -4x + -2.4x = -6.4x 1 + -6.4x + 4x2 = 2.4x + -2.4x Combine like terms: 2.4x + -2.4x = 0.0 1 + -6.4x + 4x2 = 0.0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + -1.6x + x2 = 0.0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.6x + -0.25 + x2 = 0.0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.6x + x2 = 0.0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.6x + x2 = 0.0 + -0.25 -1.6x + x2 = 0.0 + -0.25 Combine like terms: 0.0 + -0.25 = -0.25 -1.6x + x2 = -0.25 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = -0.25 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = -0.25 + 0.64 Combine like terms: -0.25 + 0.64 = 0.39 0.64 + -1.6x + x2 = 0.39 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 0.39 Calculate the square root of the right side: 0.6244998 Break this problem into two subproblems by setting (x + -0.8) equal to 0.6244998 and -0.6244998.Subproblem 1
x + -0.8 = 0.6244998 Simplifying x + -0.8 = 0.6244998 Reorder the terms: -0.8 + x = 0.6244998 Solving -0.8 + x = 0.6244998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 0.6244998 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 0.6244998 + 0.8 x = 0.6244998 + 0.8 Combine like terms: 0.6244998 + 0.8 = 1.4244998 x = 1.4244998 Simplifying x = 1.4244998Subproblem 2
x + -0.8 = -0.6244998 Simplifying x + -0.8 = -0.6244998 Reorder the terms: -0.8 + x = -0.6244998 Solving -0.8 + x = -0.6244998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -0.6244998 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -0.6244998 + 0.8 x = -0.6244998 + 0.8 Combine like terms: -0.6244998 + 0.8 = 0.1755002 x = 0.1755002 Simplifying x = 0.1755002Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4244998, 0.1755002}
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