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Simplifying -2X + 6 = X2 + 9 Reorder the terms: 6 + -2X = X2 + 9 Reorder the terms: 6 + -2X = 9 + X2 Solving 6 + -2X = 9 + X2 Solving for variable 'X'. Reorder the terms: 6 + -9 + -2X + -1X2 = 9 + X2 + -9 + -1X2 Combine like terms: 6 + -9 = -3 -3 + -2X + -1X2 = 9 + X2 + -9 + -1X2 Reorder the terms: -3 + -2X + -1X2 = 9 + -9 + X2 + -1X2 Combine like terms: 9 + -9 = 0 -3 + -2X + -1X2 = 0 + X2 + -1X2 -3 + -2X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 -3 + -2X + -1X2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 2X + X2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 2X + X2)' equal to zero and attempt to solve: Simplifying 3 + 2X + X2 = 0 Solving 3 + 2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 2X + -3 + X2 = 0 + -3 Reorder the terms: 3 + -3 + 2X + X2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2X + X2 = 0 + -3 2X + X2 = 0 + -3 Combine like terms: 0 + -3 = -3 2X + X2 = -3 The X term is 2X. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2X + 1 + X2 = -3 + 1 Reorder the terms: 1 + 2X + X2 = -3 + 1 Combine like terms: -3 + 1 = -2 1 + 2X + X2 = -2 Factor a perfect square on the left side: (X + 1)(X + 1) = -2 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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