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Simplifying X = X2 + 15X + 50 Reorder the terms: X = 50 + 15X + X2 Solving X = 50 + 15X + X2 Solving for variable 'X'. Reorder the terms: -50 + X + -15X + -1X2 = 50 + 15X + X2 + -50 + -15X + -1X2 Combine like terms: X + -15X = -14X -50 + -14X + -1X2 = 50 + 15X + X2 + -50 + -15X + -1X2 Reorder the terms: -50 + -14X + -1X2 = 50 + -50 + 15X + -15X + X2 + -1X2 Combine like terms: 50 + -50 = 0 -50 + -14X + -1X2 = 0 + 15X + -15X + X2 + -1X2 -50 + -14X + -1X2 = 15X + -15X + X2 + -1X2 Combine like terms: 15X + -15X = 0 -50 + -14X + -1X2 = 0 + X2 + -1X2 -50 + -14X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 -50 + -14X + -1X2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(50 + 14X + X2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(50 + 14X + X2)' equal to zero and attempt to solve: Simplifying 50 + 14X + X2 = 0 Solving 50 + 14X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + 14X + -50 + X2 = 0 + -50 Reorder the terms: 50 + -50 + 14X + X2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + 14X + X2 = 0 + -50 14X + X2 = 0 + -50 Combine like terms: 0 + -50 = -50 14X + X2 = -50 The X term is 14X. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14X + 49 + X2 = -50 + 49 Reorder the terms: 49 + 14X + X2 = -50 + 49 Combine like terms: -50 + 49 = -1 49 + 14X + X2 = -1 Factor a perfect square on the left side: (X + 7)(X + 7) = -1 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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