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Simplifying 2x2 + 4x + 4 = 60 Reorder the terms: 4 + 4x + 2x2 = 60 Solving 4 + 4x + 2x2 = 60 Solving for variable 'x'. Reorder the terms: 4 + -60 + 4x + 2x2 = 60 + -60 Combine like terms: 4 + -60 = -56 -56 + 4x + 2x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -56 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-28 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-28 + 2x + x2)' equal to zero and attempt to solve: Simplifying -28 + 2x + x2 = 0 Solving -28 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 2x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 2x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 2x + x2 = 0 + 28 2x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 2x + x2 = 28 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 = 28 + 1 Reorder the terms: 1 + 2x + x2 = 28 + 1 Combine like terms: 28 + 1 = 29 1 + 2x + x2 = 29 Factor a perfect square on the left side: (x + 1)(x + 1) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + 1) equal to 5.385164807 and -5.385164807.Subproblem 1
x + 1 = 5.385164807 Simplifying x + 1 = 5.385164807 Reorder the terms: 1 + x = 5.385164807 Solving 1 + x = 5.385164807 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 = 5.385164807 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.385164807 + -1 x = 5.385164807 + -1 Combine like terms: 5.385164807 + -1 = 4.385164807 x = 4.385164807 Simplifying x = 4.385164807Subproblem 2
x + 1 = -5.385164807 Simplifying x + 1 = -5.385164807 Reorder the terms: 1 + x = -5.385164807 Solving 1 + x = -5.385164807 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 = -5.385164807 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.385164807 + -1 x = -5.385164807 + -1 Combine like terms: -5.385164807 + -1 = -6.385164807 x = -6.385164807 Simplifying x = -6.385164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.385164807, -6.385164807}Solution
x = {4.385164807, -6.385164807}
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