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Simplifying 2(x + -6)(x + -6) + 40 = 0 Reorder the terms: 2(-6 + x)(x + -6) + 40 = 0 Reorder the terms: 2(-6 + x)(-6 + x) + 40 = 0 Multiply (-6 + x) * (-6 + x) 2(-6(-6 + x) + x(-6 + x)) + 40 = 0 2((-6 * -6 + x * -6) + x(-6 + x)) + 40 = 0 2((36 + -6x) + x(-6 + x)) + 40 = 0 2(36 + -6x + (-6 * x + x * x)) + 40 = 0 2(36 + -6x + (-6x + x2)) + 40 = 0 Combine like terms: -6x + -6x = -12x 2(36 + -12x + x2) + 40 = 0 (36 * 2 + -12x * 2 + x2 * 2) + 40 = 0 (72 + -24x + 2x2) + 40 = 0 Reorder the terms: 72 + 40 + -24x + 2x2 = 0 Combine like terms: 72 + 40 = 112 112 + -24x + 2x2 = 0 Solving 112 + -24x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(56 + -12x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(56 + -12x + x2)' equal to zero and attempt to solve: Simplifying 56 + -12x + x2 = 0 Solving 56 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + -12x + -56 + x2 = 0 + -56 Reorder the terms: 56 + -56 + -12x + x2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + -12x + x2 = 0 + -56 -12x + x2 = 0 + -56 Combine like terms: 0 + -56 = -56 -12x + x2 = -56 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 = -56 + 36 Reorder the terms: 36 + -12x + x2 = -56 + 36 Combine like terms: -56 + 36 = -20 36 + -12x + x2 = -20 Factor a perfect square on the left side: (x + -6)(x + -6) = -20 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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