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Simplifying (3 + 3x)(6 + -1x) = 510 Multiply (3 + 3x) * (6 + -1x) (3(6 + -1x) + 3x * (6 + -1x)) = 510 ((6 * 3 + -1x * 3) + 3x * (6 + -1x)) = 510 ((18 + -3x) + 3x * (6 + -1x)) = 510 (18 + -3x + (6 * 3x + -1x * 3x)) = 510 (18 + -3x + (18x + -3x2)) = 510 Combine like terms: -3x + 18x = 15x (18 + 15x + -3x2) = 510 Solving 18 + 15x + -3x2 = 510 Solving for variable 'x'. Reorder the terms: 18 + -510 + 15x + -3x2 = 510 + -510 Combine like terms: 18 + -510 = -492 -492 + 15x + -3x2 = 510 + -510 Combine like terms: 510 + -510 = 0 -492 + 15x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-164 + 5x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-164 + 5x + -1x2)' equal to zero and attempt to solve: Simplifying -164 + 5x + -1x2 = 0 Solving -164 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 164 + -5x + x2 = 0 Move the constant term to the right: Add '-164' to each side of the equation. 164 + -5x + -164 + x2 = 0 + -164 Reorder the terms: 164 + -164 + -5x + x2 = 0 + -164 Combine like terms: 164 + -164 = 0 0 + -5x + x2 = 0 + -164 -5x + x2 = 0 + -164 Combine like terms: 0 + -164 = -164 -5x + x2 = -164 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -164 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -164 + 6.25 Combine like terms: -164 + 6.25 = -157.75 6.25 + -5x + x2 = -157.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = -157.75 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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