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Simplifying 0 = (2x2 + 6x + 648) Reorder the terms: 0 = (648 + 6x + 2x2) Remove parenthesis around (648 + 6x + 2x2) 0 = 648 + 6x + 2x2 Solving 0 = 648 + 6x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -648 = -648 -648 + -6x + -2x2 = 648 + 6x + 2x2 + -648 + -6x + -2x2 Reorder the terms: -648 + -6x + -2x2 = 648 + -648 + 6x + -6x + 2x2 + -2x2 Combine like terms: 648 + -648 = 0 -648 + -6x + -2x2 = 0 + 6x + -6x + 2x2 + -2x2 -648 + -6x + -2x2 = 6x + -6x + 2x2 + -2x2 Combine like terms: 6x + -6x = 0 -648 + -6x + -2x2 = 0 + 2x2 + -2x2 -648 + -6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -648 + -6x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(324 + 3x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(324 + 3x + x2)' equal to zero and attempt to solve: Simplifying 324 + 3x + x2 = 0 Solving 324 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-324' to each side of the equation. 324 + 3x + -324 + x2 = 0 + -324 Reorder the terms: 324 + -324 + 3x + x2 = 0 + -324 Combine like terms: 324 + -324 = 0 0 + 3x + x2 = 0 + -324 3x + x2 = 0 + -324 Combine like terms: 0 + -324 = -324 3x + x2 = -324 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -324 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -324 + 2.25 Combine like terms: -324 + 2.25 = -321.75 2.25 + 3x + x2 = -321.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -321.75 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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