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Simplifying 2x(x + 2) + 2 = 96 Reorder the terms: 2x(2 + x) + 2 = 96 (2 * 2x + x * 2x) + 2 = 96 (4x + 2x2) + 2 = 96 Reorder the terms: 2 + 4x + 2x2 = 96 Solving 2 + 4x + 2x2 = 96 Solving for variable 'x'. Reorder the terms: 2 + -96 + 4x + 2x2 = 96 + -96 Combine like terms: 2 + -96 = -94 -94 + 4x + 2x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -94 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-47 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-47 + 2x + x2)' equal to zero and attempt to solve: Simplifying -47 + 2x + x2 = 0 Solving -47 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + 2x + 47 + x2 = 0 + 47 Reorder the terms: -47 + 47 + 2x + x2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 2x + x2 = 0 + 47 2x + x2 = 0 + 47 Combine like terms: 0 + 47 = 47 2x + x2 = 47 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 47 + 1 Reorder the terms: 1 + 2x + x2 = 47 + 1 Combine like terms: 47 + 1 = 48 1 + 2x + x2 = 48 Factor a perfect square on the left side: (x + 1)(x + 1) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + 1) equal to 6.92820323 and -6.92820323.Subproblem 1
x + 1 = 6.92820323 Simplifying x + 1 = 6.92820323 Reorder the terms: 1 + x = 6.92820323 Solving 1 + x = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 6.92820323 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.92820323 + -1 x = 6.92820323 + -1 Combine like terms: 6.92820323 + -1 = 5.92820323 x = 5.92820323 Simplifying x = 5.92820323Subproblem 2
x + 1 = -6.92820323 Simplifying x + 1 = -6.92820323 Reorder the terms: 1 + x = -6.92820323 Solving 1 + x = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -6.92820323 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.92820323 + -1 x = -6.92820323 + -1 Combine like terms: -6.92820323 + -1 = -7.92820323 x = -7.92820323 Simplifying x = -7.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.92820323, -7.92820323}Solution
x = {5.92820323, -7.92820323}
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