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Simplifying 2x[(x + 7) + 2] + 42 = 0 Reorder the terms: 2x[(7 + x) + 2] + 42 = 0 Remove parenthesis around (7 + x) 2x[7 + x + 2] + 42 = 0 Reorder the terms: 2x[7 + 2 + x] + 42 = 0 Combine like terms: 7 + 2 = 9 2x[9 + x] + 42 = 0 [9 * 2x + x * 2x] + 42 = 0 [18x + 2x2] + 42 = 0 Reorder the terms: 42 + 18x + 2x2 = 0 Solving 42 + 18x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + 9x + x2)' equal to zero and attempt to solve: Simplifying 21 + 9x + x2 = 0 Solving 21 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 9x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + 9x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 9x + x2 = 0 + -21 9x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 9x + x2 = -21 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -21 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -21 + 20.25 Combine like terms: -21 + 20.25 = -0.75 20.25 + 9x + x2 = -0.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = -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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