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Simplifying (5x + -1)(5x + -1) = 12 Reorder the terms: (-1 + 5x)(5x + -1) = 12 Reorder the terms: (-1 + 5x)(-1 + 5x) = 12 Multiply (-1 + 5x) * (-1 + 5x) (-1(-1 + 5x) + 5x * (-1 + 5x)) = 12 ((-1 * -1 + 5x * -1) + 5x * (-1 + 5x)) = 12 ((1 + -5x) + 5x * (-1 + 5x)) = 12 (1 + -5x + (-1 * 5x + 5x * 5x)) = 12 (1 + -5x + (-5x + 25x2)) = 12 Combine like terms: -5x + -5x = -10x (1 + -10x + 25x2) = 12 Solving 1 + -10x + 25x2 = 12 Solving for variable 'x'. Reorder the terms: 1 + -12 + -10x + 25x2 = 12 + -12 Combine like terms: 1 + -12 = -11 -11 + -10x + 25x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -11 + -10x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.44 + -0.4x + x2 = 0 Move the constant term to the right: Add '0.44' to each side of the equation. -0.44 + -0.4x + 0.44 + x2 = 0 + 0.44 Reorder the terms: -0.44 + 0.44 + -0.4x + x2 = 0 + 0.44 Combine like terms: -0.44 + 0.44 = 0.00 0.00 + -0.4x + x2 = 0 + 0.44 -0.4x + x2 = 0 + 0.44 Combine like terms: 0 + 0.44 = 0.44 -0.4x + x2 = 0.44 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 = 0.44 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.44 + 0.04 Combine like terms: 0.44 + 0.04 = 0.48 0.04 + -0.4x + x2 = 0.48 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.48 Calculate the square root of the right side: 0.692820323 Break this problem into two subproblems by setting (x + -0.2) equal to 0.692820323 and -0.692820323.Subproblem 1
x + -0.2 = 0.692820323 Simplifying x + -0.2 = 0.692820323 Reorder the terms: -0.2 + x = 0.692820323 Solving -0.2 + x = 0.692820323 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 = 0.692820323 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.692820323 + 0.2 x = 0.692820323 + 0.2 Combine like terms: 0.692820323 + 0.2 = 0.892820323 x = 0.892820323 Simplifying x = 0.892820323Subproblem 2
x + -0.2 = -0.692820323 Simplifying x + -0.2 = -0.692820323 Reorder the terms: -0.2 + x = -0.692820323 Solving -0.2 + x = -0.692820323 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 = -0.692820323 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.692820323 + 0.2 x = -0.692820323 + 0.2 Combine like terms: -0.692820323 + 0.2 = -0.492820323 x = -0.492820323 Simplifying x = -0.492820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.892820323, -0.492820323}
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