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Simplifying 6x(x + -6) + 6 = 8(x + 2 + -12) Reorder the terms: 6x(-6 + x) + 6 = 8(x + 2 + -12) (-6 * 6x + x * 6x) + 6 = 8(x + 2 + -12) (-36x + 6x2) + 6 = 8(x + 2 + -12) Reorder the terms: 6 + -36x + 6x2 = 8(x + 2 + -12) Reorder the terms: 6 + -36x + 6x2 = 8(2 + -12 + x) Combine like terms: 2 + -12 = -10 6 + -36x + 6x2 = 8(-10 + x) 6 + -36x + 6x2 = (-10 * 8 + x * 8) 6 + -36x + 6x2 = (-80 + 8x) Solving 6 + -36x + 6x2 = -80 + 8x Solving for variable 'x'. Reorder the terms: 6 + 80 + -36x + -8x + 6x2 = -80 + 8x + 80 + -8x Combine like terms: 6 + 80 = 86 86 + -36x + -8x + 6x2 = -80 + 8x + 80 + -8x Combine like terms: -36x + -8x = -44x 86 + -44x + 6x2 = -80 + 8x + 80 + -8x Reorder the terms: 86 + -44x + 6x2 = -80 + 80 + 8x + -8x Combine like terms: -80 + 80 = 0 86 + -44x + 6x2 = 0 + 8x + -8x 86 + -44x + 6x2 = 8x + -8x Combine like terms: 8x + -8x = 0 86 + -44x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(43 + -22x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(43 + -22x + 3x2)' equal to zero and attempt to solve: Simplifying 43 + -22x + 3x2 = 0 Solving 43 + -22x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 14.33333333 + -7.333333333x + x2 = 0 Move the constant term to the right: Add '-14.33333333' to each side of the equation. 14.33333333 + -7.333333333x + -14.33333333 + x2 = 0 + -14.33333333 Reorder the terms: 14.33333333 + -14.33333333 + -7.333333333x + x2 = 0 + -14.33333333 Combine like terms: 14.33333333 + -14.33333333 = 0.00000000 0.00000000 + -7.333333333x + x2 = 0 + -14.33333333 -7.333333333x + x2 = 0 + -14.33333333 Combine like terms: 0 + -14.33333333 = -14.33333333 -7.333333333x + x2 = -14.33333333 The x term is -7.333333333x. Take half its coefficient (-3.666666667). Square it (13.44444445) and add it to both sides. Add '13.44444445' to each side of the equation. -7.333333333x + 13.44444445 + x2 = -14.33333333 + 13.44444445 Reorder the terms: 13.44444445 + -7.333333333x + x2 = -14.33333333 + 13.44444445 Combine like terms: -14.33333333 + 13.44444445 = -0.88888888 13.44444445 + -7.333333333x + x2 = -0.88888888 Factor a perfect square on the left side: (x + -3.666666667)(x + -3.666666667) = -0.88888888 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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