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Simplifying 2x2 + 4x + 2 = 60 Reorder the terms: 2 + 4x + 2x2 = 60 Solving 2 + 4x + 2x2 = 60 Solving for variable 'x'. Reorder the terms: 2 + -60 + 4x + 2x2 = 60 + -60 Combine like terms: 2 + -60 = -58 -58 + 4x + 2x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -58 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-29 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-29 + 2x + x2)' equal to zero and attempt to solve: Simplifying -29 + 2x + x2 = 0 Solving -29 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 2x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 2x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 2x + x2 = 0 + 29 2x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 2x + x2 = 29 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 = 29 + 1 Reorder the terms: 1 + 2x + x2 = 29 + 1 Combine like terms: 29 + 1 = 30 1 + 2x + x2 = 30 Factor a perfect square on the left side: (x + 1)(x + 1) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + 1) equal to 5.477225575 and -5.477225575.Subproblem 1
x + 1 = 5.477225575 Simplifying x + 1 = 5.477225575 Reorder the terms: 1 + x = 5.477225575 Solving 1 + x = 5.477225575 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 = 5.477225575 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.477225575 + -1 x = 5.477225575 + -1 Combine like terms: 5.477225575 + -1 = 4.477225575 x = 4.477225575 Simplifying x = 4.477225575Subproblem 2
x + 1 = -5.477225575 Simplifying x + 1 = -5.477225575 Reorder the terms: 1 + x = -5.477225575 Solving 1 + x = -5.477225575 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 = -5.477225575 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.477225575 + -1 x = -5.477225575 + -1 Combine like terms: -5.477225575 + -1 = -6.477225575 x = -6.477225575 Simplifying x = -6.477225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.477225575, -6.477225575}Solution
x = {4.477225575, -6.477225575}
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