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Simplifying 3(x + -6)(x + -6) + 6 = 0 Reorder the terms: 3(-6 + x)(x + -6) + 6 = 0 Reorder the terms: 3(-6 + x)(-6 + x) + 6 = 0 Multiply (-6 + x) * (-6 + x) 3(-6(-6 + x) + x(-6 + x)) + 6 = 0 3((-6 * -6 + x * -6) + x(-6 + x)) + 6 = 0 3((36 + -6x) + x(-6 + x)) + 6 = 0 3(36 + -6x + (-6 * x + x * x)) + 6 = 0 3(36 + -6x + (-6x + x2)) + 6 = 0 Combine like terms: -6x + -6x = -12x 3(36 + -12x + x2) + 6 = 0 (36 * 3 + -12x * 3 + x2 * 3) + 6 = 0 (108 + -36x + 3x2) + 6 = 0 Reorder the terms: 108 + 6 + -36x + 3x2 = 0 Combine like terms: 108 + 6 = 114 114 + -36x + 3x2 = 0 Solving 114 + -36x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(38 + -12x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(38 + -12x + x2)' equal to zero and attempt to solve: Simplifying 38 + -12x + x2 = 0 Solving 38 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-38' to each side of the equation. 38 + -12x + -38 + x2 = 0 + -38 Reorder the terms: 38 + -38 + -12x + x2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + -12x + x2 = 0 + -38 -12x + x2 = 0 + -38 Combine like terms: 0 + -38 = -38 -12x + x2 = -38 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -38 + 36 Reorder the terms: 36 + -12x + x2 = -38 + 36 Combine like terms: -38 + 36 = -2 36 + -12x + x2 = -2 Factor a perfect square on the left side: (x + -6)(x + -6) = -2 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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