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Simplifying (4 + -2c)(4 + -2c) + 4 = 0 Multiply (4 + -2c) * (4 + -2c) (4(4 + -2c) + -2c * (4 + -2c)) + 4 = 0 ((4 * 4 + -2c * 4) + -2c * (4 + -2c)) + 4 = 0 ((16 + -8c) + -2c * (4 + -2c)) + 4 = 0 (16 + -8c + (4 * -2c + -2c * -2c)) + 4 = 0 (16 + -8c + (-8c + 4c2)) + 4 = 0 Combine like terms: -8c + -8c = -16c (16 + -16c + 4c2) + 4 = 0 Reorder the terms: 16 + 4 + -16c + 4c2 = 0 Combine like terms: 16 + 4 = 20 20 + -16c + 4c2 = 0 Solving 20 + -16c + 4c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + -4c + c2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -4c + c2)' equal to zero and attempt to solve: Simplifying 5 + -4c + c2 = 0 Solving 5 + -4c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -4c + -5 + c2 = 0 + -5 Reorder the terms: 5 + -5 + -4c + c2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4c + c2 = 0 + -5 -4c + c2 = 0 + -5 Combine like terms: 0 + -5 = -5 -4c + c2 = -5 The c term is -4c. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4c + 4 + c2 = -5 + 4 Reorder the terms: 4 + -4c + c2 = -5 + 4 Combine like terms: -5 + 4 = -1 4 + -4c + c2 = -1 Factor a perfect square on the left side: (c + -2)(c + -2) = -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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