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Simplifying (5x + -1)(5x + -1) = 48 Reorder the terms: (-1 + 5x)(5x + -1) = 48 Reorder the terms: (-1 + 5x)(-1 + 5x) = 48 Multiply (-1 + 5x) * (-1 + 5x) (-1(-1 + 5x) + 5x * (-1 + 5x)) = 48 ((-1 * -1 + 5x * -1) + 5x * (-1 + 5x)) = 48 ((1 + -5x) + 5x * (-1 + 5x)) = 48 (1 + -5x + (-1 * 5x + 5x * 5x)) = 48 (1 + -5x + (-5x + 25x2)) = 48 Combine like terms: -5x + -5x = -10x (1 + -10x + 25x2) = 48 Solving 1 + -10x + 25x2 = 48 Solving for variable 'x'. Reorder the terms: 1 + -48 + -10x + 25x2 = 48 + -48 Combine like terms: 1 + -48 = -47 -47 + -10x + 25x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -47 + -10x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.88 + -0.4x + x2 = 0 Move the constant term to the right: Add '1.88' to each side of the equation. -1.88 + -0.4x + 1.88 + x2 = 0 + 1.88 Reorder the terms: -1.88 + 1.88 + -0.4x + x2 = 0 + 1.88 Combine like terms: -1.88 + 1.88 = 0.00 0.00 + -0.4x + x2 = 0 + 1.88 -0.4x + x2 = 0 + 1.88 Combine like terms: 0 + 1.88 = 1.88 -0.4x + x2 = 1.88 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 = 1.88 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 1.88 + 0.04 Combine like terms: 1.88 + 0.04 = 1.92 0.04 + -0.4x + x2 = 1.92 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 1.92 Calculate the square root of the right side: 1.385640646 Break this problem into two subproblems by setting (x + -0.2) equal to 1.385640646 and -1.385640646.Subproblem 1
x + -0.2 = 1.385640646 Simplifying x + -0.2 = 1.385640646 Reorder the terms: -0.2 + x = 1.385640646 Solving -0.2 + x = 1.385640646 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 = 1.385640646 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.385640646 + 0.2 x = 1.385640646 + 0.2 Combine like terms: 1.385640646 + 0.2 = 1.585640646 x = 1.585640646 Simplifying x = 1.585640646Subproblem 2
x + -0.2 = -1.385640646 Simplifying x + -0.2 = -1.385640646 Reorder the terms: -0.2 + x = -1.385640646 Solving -0.2 + x = -1.385640646 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 = -1.385640646 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.385640646 + 0.2 x = -1.385640646 + 0.2 Combine like terms: -1.385640646 + 0.2 = -1.185640646 x = -1.185640646 Simplifying x = -1.185640646Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.585640646, -1.185640646}
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