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Simplifying 2x2 + 8x + 16 = 38 Reorder the terms: 16 + 8x + 2x2 = 38 Solving 16 + 8x + 2x2 = 38 Solving for variable 'x'. Reorder the terms: 16 + -38 + 8x + 2x2 = 38 + -38 Combine like terms: 16 + -38 = -22 -22 + 8x + 2x2 = 38 + -38 Combine like terms: 38 + -38 = 0 -22 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + 4x + x2)' equal to zero and attempt to solve: Simplifying -11 + 4x + x2 = 0 Solving -11 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 4x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 4x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 4x + x2 = 0 + 11 4x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 4x + x2 = 11 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 11 + 4 Reorder the terms: 4 + 4x + x2 = 11 + 4 Combine like terms: 11 + 4 = 15 4 + 4x + x2 = 15 Factor a perfect square on the left side: (x + 2)(x + 2) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + 2) equal to 3.872983346 and -3.872983346.Subproblem 1
x + 2 = 3.872983346 Simplifying x + 2 = 3.872983346 Reorder the terms: 2 + x = 3.872983346 Solving 2 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.872983346 + -2 x = 3.872983346 + -2 Combine like terms: 3.872983346 + -2 = 1.872983346 x = 1.872983346 Simplifying x = 1.872983346Subproblem 2
x + 2 = -3.872983346 Simplifying x + 2 = -3.872983346 Reorder the terms: 2 + x = -3.872983346 Solving 2 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.872983346 + -2 x = -3.872983346 + -2 Combine like terms: -3.872983346 + -2 = -5.872983346 x = -5.872983346 Simplifying x = -5.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.872983346, -5.872983346}Solution
x = {1.872983346, -5.872983346}
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