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Simplifying 4x(3x + 6) = 2(x + -7) Reorder the terms: 4x(6 + 3x) = 2(x + -7) (6 * 4x + 3x * 4x) = 2(x + -7) (24x + 12x2) = 2(x + -7) Reorder the terms: 24x + 12x2 = 2(-7 + x) 24x + 12x2 = (-7 * 2 + x * 2) 24x + 12x2 = (-14 + 2x) Solving 24x + 12x2 = -14 + 2x Solving for variable 'x'. Reorder the terms: 14 + 24x + -2x + 12x2 = -14 + 2x + 14 + -2x Combine like terms: 24x + -2x = 22x 14 + 22x + 12x2 = -14 + 2x + 14 + -2x Reorder the terms: 14 + 22x + 12x2 = -14 + 14 + 2x + -2x Combine like terms: -14 + 14 = 0 14 + 22x + 12x2 = 0 + 2x + -2x 14 + 22x + 12x2 = 2x + -2x Combine like terms: 2x + -2x = 0 14 + 22x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 11x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 11x + 6x2)' equal to zero and attempt to solve: Simplifying 7 + 11x + 6x2 = 0 Solving 7 + 11x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.166666667 + 1.833333333x + x2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + 1.833333333x + -1.166666667 + x2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + 1.833333333x + x2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + 1.833333333x + x2 = 0 + -1.166666667 1.833333333x + x2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 1.833333333x + x2 = -1.166666667 The x term is 1.833333333x. Take half its coefficient (0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. 1.833333333x + 0.8402777775 + x2 = -1.166666667 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333x + x2 = -1.166666667 + 0.8402777775 Combine like terms: -1.166666667 + 0.8402777775 = -0.3263888895 0.8402777775 + 1.833333333x + x2 = -0.3263888895 Factor a perfect square on the left side: (x + 0.9166666665)(x + 0.9166666665) = -0.3263888895 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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