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Simplifying (5x + -1)(5x + -1) = 10x + 2 Reorder the terms: (-1 + 5x)(5x + -1) = 10x + 2 Reorder the terms: (-1 + 5x)(-1 + 5x) = 10x + 2 Multiply (-1 + 5x) * (-1 + 5x) (-1(-1 + 5x) + 5x * (-1 + 5x)) = 10x + 2 ((-1 * -1 + 5x * -1) + 5x * (-1 + 5x)) = 10x + 2 ((1 + -5x) + 5x * (-1 + 5x)) = 10x + 2 (1 + -5x + (-1 * 5x + 5x * 5x)) = 10x + 2 (1 + -5x + (-5x + 25x2)) = 10x + 2 Combine like terms: -5x + -5x = -10x (1 + -10x + 25x2) = 10x + 2 Reorder the terms: 1 + -10x + 25x2 = 2 + 10x Solving 1 + -10x + 25x2 = 2 + 10x Solving for variable 'x'. Reorder the terms: 1 + -2 + -10x + -10x + 25x2 = 2 + 10x + -2 + -10x Combine like terms: 1 + -2 = -1 -1 + -10x + -10x + 25x2 = 2 + 10x + -2 + -10x Combine like terms: -10x + -10x = -20x -1 + -20x + 25x2 = 2 + 10x + -2 + -10x Reorder the terms: -1 + -20x + 25x2 = 2 + -2 + 10x + -10x Combine like terms: 2 + -2 = 0 -1 + -20x + 25x2 = 0 + 10x + -10x -1 + -20x + 25x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -1 + -20x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.04 + -0.8x + x2 = 0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + -0.8x + 0.04 + x2 = 0 + 0.04 Reorder the terms: -0.04 + 0.04 + -0.8x + x2 = 0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + -0.8x + x2 = 0 + 0.04 -0.8x + x2 = 0 + 0.04 Combine like terms: 0 + 0.04 = 0.04 -0.8x + x2 = 0.04 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 0.04 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 0.04 + 0.16 Combine like terms: 0.04 + 0.16 = 0.2 0.16 + -0.8x + x2 = 0.2 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 0.2 Calculate the square root of the right side: 0.447213596 Break this problem into two subproblems by setting (x + -0.4) equal to 0.447213596 and -0.447213596.Subproblem 1
x + -0.4 = 0.447213596 Simplifying x + -0.4 = 0.447213596 Reorder the terms: -0.4 + x = 0.447213596 Solving -0.4 + x = 0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.447213596 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.447213596 + 0.4 x = 0.447213596 + 0.4 Combine like terms: 0.447213596 + 0.4 = 0.847213596 x = 0.847213596 Simplifying x = 0.847213596Subproblem 2
x + -0.4 = -0.447213596 Simplifying x + -0.4 = -0.447213596 Reorder the terms: -0.4 + x = -0.447213596 Solving -0.4 + x = -0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -0.447213596 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.447213596 + 0.4 x = -0.447213596 + 0.4 Combine like terms: -0.447213596 + 0.4 = -0.047213596 x = -0.047213596 Simplifying x = -0.047213596Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.847213596, -0.047213596}
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