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Simplifying 6(4x + -3) + 20x + -24x2 = 14 Reorder the terms: 6(-3 + 4x) + 20x + -24x2 = 14 (-3 * 6 + 4x * 6) + 20x + -24x2 = 14 (-18 + 24x) + 20x + -24x2 = 14 Combine like terms: 24x + 20x = 44x -18 + 44x + -24x2 = 14 Solving -18 + 44x + -24x2 = 14 Solving for variable 'x'. Reorder the terms: -18 + -14 + 44x + -24x2 = 14 + -14 Combine like terms: -18 + -14 = -32 -32 + 44x + -24x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -32 + 44x + -24x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + 11x + -6x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-8 + 11x + -6x2)' equal to zero and attempt to solve: Simplifying -8 + 11x + -6x2 = 0 Solving -8 + 11x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 1.333333333 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -1.833333333x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -1.833333333x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -1.833333333x + x2 = 0 + -1.333333333 -1.833333333x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -1.833333333x + x2 = -1.333333333 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 = -1.333333333 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = -1.333333333 + 0.8402777775 Combine like terms: -1.333333333 + 0.8402777775 = -0.4930555555 0.8402777775 + -1.833333333x + x2 = -0.4930555555 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = -0.4930555555 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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