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Simplifying -2x(4 + 3x) = 13 (4 * -2x + 3x * -2x) = 13 (-8x + -6x2) = 13 Solving -8x + -6x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + -8x + -6x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -8x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 8x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 8x + 6x2)' equal to zero and attempt to solve: Simplifying 13 + 8x + 6x2 = 0 Solving 13 + 8x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.166666667 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-2.166666667' to each side of the equation. 2.166666667 + 1.333333333x + -2.166666667 + x2 = 0 + -2.166666667 Reorder the terms: 2.166666667 + -2.166666667 + 1.333333333x + x2 = 0 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + 1.333333333x + x2 = 0 + -2.166666667 1.333333333x + x2 = 0 + -2.166666667 Combine like terms: 0 + -2.166666667 = -2.166666667 1.333333333x + x2 = -2.166666667 The x term is 1.333333333x. 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. 1.333333333x + 0.4444444442 + x2 = -2.166666667 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -2.166666667 + 0.4444444442 Combine like terms: -2.166666667 + 0.4444444442 = -1.7222222228 0.4444444442 + 1.333333333x + x2 = -1.7222222228 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = -1.7222222228 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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