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Simplifying 4(x2) + (8x) + 8 = 0 Reorder the terms: 8 + (8x) + 4x2 = 0 Solving 8 + (8x) + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + (2x) + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + (2x) + x2)' equal to zero and attempt to solve: Simplifying 2 + (2x) + x2 = 0 Solving 2 + (2x) + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + (2x) + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + (2x) + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + (2x) + x2 = 0 + -2 (2x) + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 (2x) + x2 = -2 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 = -2 + 1 Reorder the terms: 1 + (2x) + x2 = -2 + 1 Combine like terms: -2 + 1 = -1 1 + (2x) + x2 = -1 Factor a perfect square on the left side: (x + 1)(x + 1) = -1 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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