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Simplifying (5x + 2)(5x + 2) = 48 Reorder the terms: (2 + 5x)(5x + 2) = 48 Reorder the terms: (2 + 5x)(2 + 5x) = 48 Multiply (2 + 5x) * (2 + 5x) (2(2 + 5x) + 5x * (2 + 5x)) = 48 ((2 * 2 + 5x * 2) + 5x * (2 + 5x)) = 48 ((4 + 10x) + 5x * (2 + 5x)) = 48 (4 + 10x + (2 * 5x + 5x * 5x)) = 48 (4 + 10x + (10x + 25x2)) = 48 Combine like terms: 10x + 10x = 20x (4 + 20x + 25x2) = 48 Solving 4 + 20x + 25x2 = 48 Solving for variable 'x'. Reorder the terms: 4 + -48 + 20x + 25x2 = 48 + -48 Combine like terms: 4 + -48 = -44 -44 + 20x + 25x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -44 + 20x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.76 + 0.8x + x2 = 0 Move the constant term to the right: Add '1.76' to each side of the equation. -1.76 + 0.8x + 1.76 + x2 = 0 + 1.76 Reorder the terms: -1.76 + 1.76 + 0.8x + x2 = 0 + 1.76 Combine like terms: -1.76 + 1.76 = 0.00 0.00 + 0.8x + x2 = 0 + 1.76 0.8x + x2 = 0 + 1.76 Combine like terms: 0 + 1.76 = 1.76 0.8x + x2 = 1.76 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 = 1.76 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 1.76 + 0.16 Combine like terms: 1.76 + 0.16 = 1.92 0.16 + 0.8x + x2 = 1.92 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 1.92 Calculate the square root of the right side: 1.385640646 Break this problem into two subproblems by setting (x + 0.4) equal to 1.385640646 and -1.385640646.Subproblem 1
x + 0.4 = 1.385640646 Simplifying x + 0.4 = 1.385640646 Reorder the terms: 0.4 + x = 1.385640646 Solving 0.4 + x = 1.385640646 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 = 1.385640646 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.385640646 + -0.4 x = 1.385640646 + -0.4 Combine like terms: 1.385640646 + -0.4 = 0.985640646 x = 0.985640646 Simplifying x = 0.985640646Subproblem 2
x + 0.4 = -1.385640646 Simplifying x + 0.4 = -1.385640646 Reorder the terms: 0.4 + x = -1.385640646 Solving 0.4 + x = -1.385640646 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 = -1.385640646 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.385640646 + -0.4 x = -1.385640646 + -0.4 Combine like terms: -1.385640646 + -0.4 = -1.785640646 x = -1.785640646 Simplifying x = -1.785640646Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.985640646, -1.785640646}
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