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Simplifying 6x2 + 64x + 1024 = 0 Reorder the terms: 1024 + 64x + 6x2 = 0 Solving 1024 + 64x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(512 + 32x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(512 + 32x + 3x2)' equal to zero and attempt to solve: Simplifying 512 + 32x + 3x2 = 0 Solving 512 + 32x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 170.6666667 + 10.66666667x + x2 = 0 Move the constant term to the right: Add '-170.6666667' to each side of the equation. 170.6666667 + 10.66666667x + -170.6666667 + x2 = 0 + -170.6666667 Reorder the terms: 170.6666667 + -170.6666667 + 10.66666667x + x2 = 0 + -170.6666667 Combine like terms: 170.6666667 + -170.6666667 = 0.0000000 0.0000000 + 10.66666667x + x2 = 0 + -170.6666667 10.66666667x + x2 = 0 + -170.6666667 Combine like terms: 0 + -170.6666667 = -170.6666667 10.66666667x + x2 = -170.6666667 The x term is 10.66666667x. Take half its coefficient (5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. 10.66666667x + 28.44444446 + x2 = -170.6666667 + 28.44444446 Reorder the terms: 28.44444446 + 10.66666667x + x2 = -170.6666667 + 28.44444446 Combine like terms: -170.6666667 + 28.44444446 = -142.22222224 28.44444446 + 10.66666667x + x2 = -142.22222224 Factor a perfect square on the left side: (x + 5.333333335)(x + 5.333333335) = -142.22222224 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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