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Simplifying (8X2 + -2X + 7) + -1(2X2 + -4X + -7) = 0 Reorder the terms: (7 + -2X + 8X2) + -1(2X2 + -4X + -7) = 0 Remove parenthesis around (7 + -2X + 8X2) 7 + -2X + 8X2 + -1(2X2 + -4X + -7) = 0 Reorder the terms: 7 + -2X + 8X2 + -1(-7 + -4X + 2X2) = 0 7 + -2X + 8X2 + (-7 * -1 + -4X * -1 + 2X2 * -1) = 0 7 + -2X + 8X2 + (7 + 4X + -2X2) = 0 Reorder the terms: 7 + 7 + -2X + 4X + 8X2 + -2X2 = 0 Combine like terms: 7 + 7 = 14 14 + -2X + 4X + 8X2 + -2X2 = 0 Combine like terms: -2X + 4X = 2X 14 + 2X + 8X2 + -2X2 = 0 Combine like terms: 8X2 + -2X2 = 6X2 14 + 2X + 6X2 = 0 Solving 14 + 2X + 6X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + X + 3X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + X + 3X2)' equal to zero and attempt to solve: Simplifying 7 + X + 3X2 = 0 Solving 7 + X + 3X2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + 0.3333333333X + X2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + 0.3333333333X + -2.333333333 + X2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + 0.3333333333X + X2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + 0.3333333333X + X2 = 0 + -2.333333333 0.3333333333X + X2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 0.3333333333X + X2 = -2.333333333 The X term is X. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333X + 0.25 + X2 = -2.333333333 + 0.25 Reorder the terms: 0.25 + 0.3333333333X + X2 = -2.333333333 + 0.25 Combine like terms: -2.333333333 + 0.25 = -2.083333333 0.25 + 0.3333333333X + X2 = -2.083333333 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = -2.083333333 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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