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Simplifying -8 = 2x2 + 4x + 8 Reorder the terms: -8 = 8 + 4x + 2x2 Solving -8 = 8 + 4x + 2x2 Solving for variable 'x'. Combine like terms: -8 + -8 = -16 -16 + -4x + -2x2 = 8 + 4x + 2x2 + -8 + -4x + -2x2 Reorder the terms: -16 + -4x + -2x2 = 8 + -8 + 4x + -4x + 2x2 + -2x2 Combine like terms: 8 + -8 = 0 -16 + -4x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2 -16 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2 Combine like terms: 4x + -4x = 0 -16 + -4x + -2x2 = 0 + 2x2 + -2x2 -16 + -4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -16 + -4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(8 + 2x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(8 + 2x + x2)' equal to zero and attempt to solve: Simplifying 8 + 2x + x2 = 0 Solving 8 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 2x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 2x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 2x + x2 = 0 + -8 2x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 2x + x2 = -8 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 = -8 + 1 Reorder the terms: 1 + 2x + x2 = -8 + 1 Combine like terms: -8 + 1 = -7 1 + 2x + x2 = -7 Factor a perfect square on the left side: (x + 1)(x + 1) = -7 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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