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Simplifying 6X2 + -42X + 78 = 0 Reorder the terms: 78 + -42X + 6X2 = 0 Solving 78 + -42X + 6X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '6'. 6(13 + -7X + X2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(13 + -7X + X2)' equal to zero and attempt to solve: Simplifying 13 + -7X + X2 = 0 Solving 13 + -7X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -7X + -13 + X2 = 0 + -13 Reorder the terms: 13 + -13 + -7X + X2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -7X + X2 = 0 + -13 -7X + X2 = 0 + -13 Combine like terms: 0 + -13 = -13 -7X + X2 = -13 The X term is -7X. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7X + 12.25 + X2 = -13 + 12.25 Reorder the terms: 12.25 + -7X + X2 = -13 + 12.25 Combine like terms: -13 + 12.25 = -0.75 12.25 + -7X + X2 = -0.75 Factor a perfect square on the left side: (X + -3.5)(X + -3.5) = -0.75 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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