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Simplifying (5x + 2)(5x + 2) = 5 Reorder the terms: (2 + 5x)(5x + 2) = 5 Reorder the terms: (2 + 5x)(2 + 5x) = 5 Multiply (2 + 5x) * (2 + 5x) (2(2 + 5x) + 5x * (2 + 5x)) = 5 ((2 * 2 + 5x * 2) + 5x * (2 + 5x)) = 5 ((4 + 10x) + 5x * (2 + 5x)) = 5 (4 + 10x + (2 * 5x + 5x * 5x)) = 5 (4 + 10x + (10x + 25x2)) = 5 Combine like terms: 10x + 10x = 20x (4 + 20x + 25x2) = 5 Solving 4 + 20x + 25x2 = 5 Solving for variable 'x'. Reorder the terms: 4 + -5 + 20x + 25x2 = 5 + -5 Combine like terms: 4 + -5 = -1 -1 + 20x + 25x2 = 5 + -5 Combine like terms: 5 + -5 = 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 = 0.047213596 x = 0.047213596 Simplifying x = 0.047213596Subproblem 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 = -0.847213596 x = -0.847213596 Simplifying x = -0.847213596Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.047213596, -0.847213596}
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