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Simplifying 2x2 + 4x + 8 = 32 Reorder the terms: 8 + 4x + 2x2 = 32 Solving 8 + 4x + 2x2 = 32 Solving for variable 'x'. Reorder the terms: 8 + -32 + 4x + 2x2 = 32 + -32 Combine like terms: 8 + -32 = -24 -24 + 4x + 2x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -24 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + 2x + x2)' equal to zero and attempt to solve: Simplifying -12 + 2x + x2 = 0 Solving -12 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 2x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 2x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 2x + x2 = 0 + 12 2x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 2x + x2 = 12 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 = 12 + 1 Reorder the terms: 1 + 2x + x2 = 12 + 1 Combine like terms: 12 + 1 = 13 1 + 2x + x2 = 13 Factor a perfect square on the left side: (x + 1)(x + 1) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + 1) equal to 3.605551275 and -3.605551275.Subproblem 1
x + 1 = 3.605551275 Simplifying x + 1 = 3.605551275 Reorder the terms: 1 + x = 3.605551275 Solving 1 + x = 3.605551275 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 = 3.605551275 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.605551275 + -1 x = 3.605551275 + -1 Combine like terms: 3.605551275 + -1 = 2.605551275 x = 2.605551275 Simplifying x = 2.605551275Subproblem 2
x + 1 = -3.605551275 Simplifying x + 1 = -3.605551275 Reorder the terms: 1 + x = -3.605551275 Solving 1 + x = -3.605551275 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 = -3.605551275 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.605551275 + -1 x = -3.605551275 + -1 Combine like terms: -3.605551275 + -1 = -4.605551275 x = -4.605551275 Simplifying x = -4.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.605551275, -4.605551275}Solution
x = {2.605551275, -4.605551275}
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