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Simplifying 6x2 + 80x + 1000 = 0 Reorder the terms: 1000 + 80x + 6x2 = 0 Solving 1000 + 80x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(500 + 40x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(500 + 40x + 3x2)' equal to zero and attempt to solve: Simplifying 500 + 40x + 3x2 = 0 Solving 500 + 40x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 166.6666667 + 13.33333333x + x2 = 0 Move the constant term to the right: Add '-166.6666667' to each side of the equation. 166.6666667 + 13.33333333x + -166.6666667 + x2 = 0 + -166.6666667 Reorder the terms: 166.6666667 + -166.6666667 + 13.33333333x + x2 = 0 + -166.6666667 Combine like terms: 166.6666667 + -166.6666667 = 0.0000000 0.0000000 + 13.33333333x + x2 = 0 + -166.6666667 13.33333333x + x2 = 0 + -166.6666667 Combine like terms: 0 + -166.6666667 = -166.6666667 13.33333333x + x2 = -166.6666667 The x term is 13.33333333x. Take half its coefficient (6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. 13.33333333x + 44.44444442 + x2 = -166.6666667 + 44.44444442 Reorder the terms: 44.44444442 + 13.33333333x + x2 = -166.6666667 + 44.44444442 Combine like terms: -166.6666667 + 44.44444442 = -122.22222228 44.44444442 + 13.33333333x + x2 = -122.22222228 Factor a perfect square on the left side: (x + 6.666666665)(x + 6.666666665) = -122.22222228 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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