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Simplifying 6x(2 + -1x) = 52 (2 * 6x + -1x * 6x) = 52 (12x + -6x2) = 52 Solving 12x + -6x2 = 52 Solving for variable 'x'. Reorder the terms: -52 + 12x + -6x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + 12x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-26 + 6x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-26 + 6x + -3x2)' equal to zero and attempt to solve: Simplifying -26 + 6x + -3x2 = 0 Solving -26 + 6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 8.666666667 + -2x + x2 = 0 Move the constant term to the right: Add '-8.666666667' to each side of the equation. 8.666666667 + -2x + -8.666666667 + x2 = 0 + -8.666666667 Reorder the terms: 8.666666667 + -8.666666667 + -2x + x2 = 0 + -8.666666667 Combine like terms: 8.666666667 + -8.666666667 = 0.000000000 0.000000000 + -2x + x2 = 0 + -8.666666667 -2x + x2 = 0 + -8.666666667 Combine like terms: 0 + -8.666666667 = -8.666666667 -2x + x2 = -8.666666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -8.666666667 + 1 Reorder the terms: 1 + -2x + x2 = -8.666666667 + 1 Combine like terms: -8.666666667 + 1 = -7.666666667 1 + -2x + x2 = -7.666666667 Factor a perfect square on the left side: (x + -1)(x + -1) = -7.666666667 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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