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Simplifying (9 + x)(2 + -1x) = 102 Multiply (9 + x) * (2 + -1x) (9(2 + -1x) + x(2 + -1x)) = 102 ((2 * 9 + -1x * 9) + x(2 + -1x)) = 102 ((18 + -9x) + x(2 + -1x)) = 102 (18 + -9x + (2 * x + -1x * x)) = 102 (18 + -9x + (2x + -1x2)) = 102 Combine like terms: -9x + 2x = -7x (18 + -7x + -1x2) = 102 Solving 18 + -7x + -1x2 = 102 Solving for variable 'x'. Reorder the terms: 18 + -102 + -7x + -1x2 = 102 + -102 Combine like terms: 18 + -102 = -84 -84 + -7x + -1x2 = 102 + -102 Combine like terms: 102 + -102 = 0 -84 + -7x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(84 + 7x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(84 + 7x + x2)' equal to zero and attempt to solve: Simplifying 84 + 7x + x2 = 0 Solving 84 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-84' to each side of the equation. 84 + 7x + -84 + x2 = 0 + -84 Reorder the terms: 84 + -84 + 7x + x2 = 0 + -84 Combine like terms: 84 + -84 = 0 0 + 7x + x2 = 0 + -84 7x + x2 = 0 + -84 Combine like terms: 0 + -84 = -84 7x + x2 = -84 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -84 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -84 + 12.25 Combine like terms: -84 + 12.25 = -71.75 12.25 + 7x + x2 = -71.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = -71.75 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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