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Simplifying m = m2 + 22m + 121 Reorder the terms: m = 121 + 22m + m2 Solving m = 121 + 22m + m2 Solving for variable 'm'. Reorder the terms: -121 + m + -22m + -1m2 = 121 + 22m + m2 + -121 + -22m + -1m2 Combine like terms: m + -22m = -21m -121 + -21m + -1m2 = 121 + 22m + m2 + -121 + -22m + -1m2 Reorder the terms: -121 + -21m + -1m2 = 121 + -121 + 22m + -22m + m2 + -1m2 Combine like terms: 121 + -121 = 0 -121 + -21m + -1m2 = 0 + 22m + -22m + m2 + -1m2 -121 + -21m + -1m2 = 22m + -22m + m2 + -1m2 Combine like terms: 22m + -22m = 0 -121 + -21m + -1m2 = 0 + m2 + -1m2 -121 + -21m + -1m2 = m2 + -1m2 Combine like terms: m2 + -1m2 = 0 -121 + -21m + -1m2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(121 + 21m + m2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(121 + 21m + m2)' equal to zero and attempt to solve: Simplifying 121 + 21m + m2 = 0 Solving 121 + 21m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-121' to each side of the equation. 121 + 21m + -121 + m2 = 0 + -121 Reorder the terms: 121 + -121 + 21m + m2 = 0 + -121 Combine like terms: 121 + -121 = 0 0 + 21m + m2 = 0 + -121 21m + m2 = 0 + -121 Combine like terms: 0 + -121 = -121 21m + m2 = -121 The m term is 21m. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21m + 110.25 + m2 = -121 + 110.25 Reorder the terms: 110.25 + 21m + m2 = -121 + 110.25 Combine like terms: -121 + 110.25 = -10.75 110.25 + 21m + m2 = -10.75 Factor a perfect square on the left side: (m + 10.5)(m + 10.5) = -10.75 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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