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Simplifying 30x2 + 52x = -164 Reorder the terms: 52x + 30x2 = -164 Solving 52x + 30x2 = -164 Solving for variable 'x'. Reorder the terms: 164 + 52x + 30x2 = -164 + 164 Combine like terms: -164 + 164 = 0 164 + 52x + 30x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(82 + 26x + 15x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(82 + 26x + 15x2)' equal to zero and attempt to solve: Simplifying 82 + 26x + 15x2 = 0 Solving 82 + 26x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 5.466666667 + 1.733333333x + x2 = 0 Move the constant term to the right: Add '-5.466666667' to each side of the equation. 5.466666667 + 1.733333333x + -5.466666667 + x2 = 0 + -5.466666667 Reorder the terms: 5.466666667 + -5.466666667 + 1.733333333x + x2 = 0 + -5.466666667 Combine like terms: 5.466666667 + -5.466666667 = 0.000000000 0.000000000 + 1.733333333x + x2 = 0 + -5.466666667 1.733333333x + x2 = 0 + -5.466666667 Combine like terms: 0 + -5.466666667 = -5.466666667 1.733333333x + x2 = -5.466666667 The x term is 1.733333333x. Take half its coefficient (0.8666666665). Square it (0.7511111108) and add it to both sides. Add '0.7511111108' to each side of the equation. 1.733333333x + 0.7511111108 + x2 = -5.466666667 + 0.7511111108 Reorder the terms: 0.7511111108 + 1.733333333x + x2 = -5.466666667 + 0.7511111108 Combine like terms: -5.466666667 + 0.7511111108 = -4.7155555562 0.7511111108 + 1.733333333x + x2 = -4.7155555562 Factor a perfect square on the left side: (x + 0.8666666665)(x + 0.8666666665) = -4.7155555562 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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