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Simplifying (5x + -1)(5x + -1) = 0.36 Reorder the terms: (-1 + 5x)(5x + -1) = 0.36 Reorder the terms: (-1 + 5x)(-1 + 5x) = 0.36 Multiply (-1 + 5x) * (-1 + 5x) (-1(-1 + 5x) + 5x * (-1 + 5x)) = 0.36 ((-1 * -1 + 5x * -1) + 5x * (-1 + 5x)) = 0.36 ((1 + -5x) + 5x * (-1 + 5x)) = 0.36 (1 + -5x + (-1 * 5x + 5x * 5x)) = 0.36 (1 + -5x + (-5x + 25x2)) = 0.36 Combine like terms: -5x + -5x = -10x (1 + -10x + 25x2) = 0.36 Solving 1 + -10x + 25x2 = 0.36 Solving for variable 'x'. Reorder the terms: 1 + -0.36 + -10x + 25x2 = 0.36 + -0.36 Combine like terms: 1 + -0.36 = 0.64 0.64 + -10x + 25x2 = 0.36 + -0.36 Combine like terms: 0.36 + -0.36 = 0.00 0.64 + -10x + 25x2 = 0.00 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.0256 + -0.4x + x2 = 0.00 Move the constant term to the right: Add '-0.0256' to each side of the equation. 0.0256 + -0.4x + -0.0256 + x2 = 0.00 + -0.0256 Reorder the terms: 0.0256 + -0.0256 + -0.4x + x2 = 0.00 + -0.0256 Combine like terms: 0.0256 + -0.0256 = 0.0000 0.0000 + -0.4x + x2 = 0.00 + -0.0256 -0.4x + x2 = 0.00 + -0.0256 Combine like terms: 0.00 + -0.0256 = -0.0256 -0.4x + x2 = -0.0256 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = -0.0256 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = -0.0256 + 0.04 Combine like terms: -0.0256 + 0.04 = 0.0144 0.04 + -0.4x + x2 = 0.0144 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.0144 Calculate the square root of the right side: 0.12 Break this problem into two subproblems by setting (x + -0.2) equal to 0.12 and -0.12.Subproblem 1
x + -0.2 = 0.12 Simplifying x + -0.2 = 0.12 Reorder the terms: -0.2 + x = 0.12 Solving -0.2 + x = 0.12 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.12 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.12 + 0.2 x = 0.12 + 0.2 Combine like terms: 0.12 + 0.2 = 0.32 x = 0.32 Simplifying x = 0.32Subproblem 2
x + -0.2 = -0.12 Simplifying x + -0.2 = -0.12 Reorder the terms: -0.2 + x = -0.12 Solving -0.2 + x = -0.12 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.12 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.12 + 0.2 x = -0.12 + 0.2 Combine like terms: -0.12 + 0.2 = 0.08 x = 0.08 Simplifying x = 0.08Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.32, 0.08}
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