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Simplifying 0 = 60 + -14x + 6x2 Solving 0 = 60 + -14x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -60 = -60 -60 + 14x + -6x2 = 60 + -14x + 6x2 + -60 + 14x + -6x2 Reorder the terms: -60 + 14x + -6x2 = 60 + -60 + -14x + 14x + 6x2 + -6x2 Combine like terms: 60 + -60 = 0 -60 + 14x + -6x2 = 0 + -14x + 14x + 6x2 + -6x2 -60 + 14x + -6x2 = -14x + 14x + 6x2 + -6x2 Combine like terms: -14x + 14x = 0 -60 + 14x + -6x2 = 0 + 6x2 + -6x2 -60 + 14x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -60 + 14x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-30 + 7x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + 7x + -3x2)' equal to zero and attempt to solve: Simplifying -30 + 7x + -3x2 = 0 Solving -30 + 7x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 10 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -2.333333333x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -2.333333333x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -2.333333333x + x2 = 0 + -10 -2.333333333x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -2.333333333x + x2 = -10 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = -10 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = -10 + 1.361111112 Combine like terms: -10 + 1.361111112 = -8.638888888 1.361111112 + -2.333333333x + x2 = -8.638888888 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = -8.638888888 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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