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Simplifying 21 = -3(x + 2)(x + -3) Reorder the terms: 21 = -3(2 + x)(x + -3) Reorder the terms: 21 = -3(2 + x)(-3 + x) Multiply (2 + x) * (-3 + x) 21 = -3(2(-3 + x) + x(-3 + x)) 21 = -3((-3 * 2 + x * 2) + x(-3 + x)) 21 = -3((-6 + 2x) + x(-3 + x)) 21 = -3(-6 + 2x + (-3 * x + x * x)) 21 = -3(-6 + 2x + (-3x + x2)) Combine like terms: 2x + -3x = -1x 21 = -3(-6 + -1x + x2) 21 = (-6 * -3 + -1x * -3 + x2 * -3) 21 = (18 + 3x + -3x2) Solving 21 = 18 + 3x + -3x2 Solving for variable 'x'. Combine like terms: 21 + -18 = 3 3 + -3x + 3x2 = 18 + 3x + -3x2 + -18 + -3x + 3x2 Reorder the terms: 3 + -3x + 3x2 = 18 + -18 + 3x + -3x + -3x2 + 3x2 Combine like terms: 18 + -18 = 0 3 + -3x + 3x2 = 0 + 3x + -3x + -3x2 + 3x2 3 + -3x + 3x2 = 3x + -3x + -3x2 + 3x2 Combine like terms: 3x + -3x = 0 3 + -3x + 3x2 = 0 + -3x2 + 3x2 3 + -3x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 3 + -3x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -1x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -1x + x2)' equal to zero and attempt to solve: Simplifying 1 + -1x + x2 = 0 Solving 1 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -1x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x + x2 = 0 + -1 -1x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1x + x2 = -1 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -1 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + -1x + x2 = -0.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -0.75 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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