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Simplifying x = 2x2 + 8x + 16 Reorder the terms: x = 16 + 8x + 2x2 Solving x = 16 + 8x + 2x2 Solving for variable 'x'. Reorder the terms: -16 + x + -8x + -2x2 = 16 + 8x + 2x2 + -16 + -8x + -2x2 Combine like terms: x + -8x = -7x -16 + -7x + -2x2 = 16 + 8x + 2x2 + -16 + -8x + -2x2 Reorder the terms: -16 + -7x + -2x2 = 16 + -16 + 8x + -8x + 2x2 + -2x2 Combine like terms: 16 + -16 = 0 -16 + -7x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2 -16 + -7x + -2x2 = 8x + -8x + 2x2 + -2x2 Combine like terms: 8x + -8x = 0 -16 + -7x + -2x2 = 0 + 2x2 + -2x2 -16 + -7x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -16 + -7x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + 7x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying 16 + 7x + 2x2 = 0 Solving 16 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8 + 3.5x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 3.5x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 3.5x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3.5x + x2 = 0 + -8 3.5x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 3.5x + x2 = -8 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = -8 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -8 + 3.0625 Combine like terms: -8 + 3.0625 = -4.9375 3.0625 + 3.5x + x2 = -4.9375 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = -4.9375 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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