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Simplifying 6p2 + 8p + 10 = 0 Reorder the terms: 10 + 8p + 6p2 = 0 Solving 10 + 8p + 6p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 4p + 3p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 4p + 3p2)' equal to zero and attempt to solve: Simplifying 5 + 4p + 3p2 = 0 Solving 5 + 4p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + 1.333333333p + p2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 1.333333333p + -1.666666667 + p2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 1.333333333p + p2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 1.333333333p + p2 = 0 + -1.666666667 1.333333333p + p2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 1.333333333p + p2 = -1.666666667 The p term is 1.333333333p. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333p + 0.4444444442 + p2 = -1.666666667 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333p + p2 = -1.666666667 + 0.4444444442 Combine like terms: -1.666666667 + 0.4444444442 = -1.2222222228 0.4444444442 + 1.333333333p + p2 = -1.2222222228 Factor a perfect square on the left side: (p + 0.6666666665)(p + 0.6666666665) = -1.2222222228 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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