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Simplifying 0 = 4x2 + 16x + 22 Reorder the terms: 0 = 22 + 16x + 4x2 Solving 0 = 22 + 16x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -22 = -22 -22 + -16x + -4x2 = 22 + 16x + 4x2 + -22 + -16x + -4x2 Reorder the terms: -22 + -16x + -4x2 = 22 + -22 + 16x + -16x + 4x2 + -4x2 Combine like terms: 22 + -22 = 0 -22 + -16x + -4x2 = 0 + 16x + -16x + 4x2 + -4x2 -22 + -16x + -4x2 = 16x + -16x + 4x2 + -4x2 Combine like terms: 16x + -16x = 0 -22 + -16x + -4x2 = 0 + 4x2 + -4x2 -22 + -16x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -22 + -16x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(11 + 8x + 2x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(11 + 8x + 2x2)' equal to zero and attempt to solve: Simplifying 11 + 8x + 2x2 = 0 Solving 11 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + 4x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + 4x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + 4x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + 4x + x2 = 0 + -5.5 4x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 4x + x2 = -5.5 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 = -5.5 + 4 Reorder the terms: 4 + 4x + x2 = -5.5 + 4 Combine like terms: -5.5 + 4 = -1.5 4 + 4x + x2 = -1.5 Factor a perfect square on the left side: (x + 2)(x + 2) = -1.5 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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