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Simplifying (5x + 4)(5x + 4) = 11 Reorder the terms: (4 + 5x)(5x + 4) = 11 Reorder the terms: (4 + 5x)(4 + 5x) = 11 Multiply (4 + 5x) * (4 + 5x) (4(4 + 5x) + 5x * (4 + 5x)) = 11 ((4 * 4 + 5x * 4) + 5x * (4 + 5x)) = 11 ((16 + 20x) + 5x * (4 + 5x)) = 11 (16 + 20x + (4 * 5x + 5x * 5x)) = 11 (16 + 20x + (20x + 25x2)) = 11 Combine like terms: 20x + 20x = 40x (16 + 40x + 25x2) = 11 Solving 16 + 40x + 25x2 = 11 Solving for variable 'x'. Reorder the terms: 16 + -11 + 40x + 25x2 = 11 + -11 Combine like terms: 16 + -11 = 5 5 + 40x + 25x2 = 11 + -11 Combine like terms: 11 + -11 = 0 5 + 40x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 8x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + 8x + 5x2)' equal to zero and attempt to solve: Simplifying 1 + 8x + 5x2 = 0 Solving 1 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 1.6x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 1.6x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 1.6x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 1.6x + x2 = 0 + -0.2 1.6x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 1.6x + x2 = -0.2 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = -0.2 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = -0.2 + 0.64 Combine like terms: -0.2 + 0.64 = 0.44 0.64 + 1.6x + x2 = 0.44 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (x + 0.8) equal to 0.663324958 and -0.663324958.Subproblem 1
x + 0.8 = 0.663324958 Simplifying x + 0.8 = 0.663324958 Reorder the terms: 0.8 + x = 0.663324958 Solving 0.8 + x = 0.663324958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 0.663324958 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 0.663324958 + -0.8 x = 0.663324958 + -0.8 Combine like terms: 0.663324958 + -0.8 = -0.136675042 x = -0.136675042 Simplifying x = -0.136675042Subproblem 2
x + 0.8 = -0.663324958 Simplifying x + 0.8 = -0.663324958 Reorder the terms: 0.8 + x = -0.663324958 Solving 0.8 + x = -0.663324958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -0.663324958 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -0.663324958 + -0.8 x = -0.663324958 + -0.8 Combine like terms: -0.663324958 + -0.8 = -1.463324958 x = -1.463324958 Simplifying x = -1.463324958Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.136675042, -1.463324958}Solution
x = {-0.136675042, -1.463324958}
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