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Simplifying -9 = x2 + 6x + 5 Reorder the terms: -9 = 5 + 6x + x2 Solving -9 = 5 + 6x + x2 Solving for variable 'x'. Combine like terms: -9 + -5 = -14 -14 + -6x + -1x2 = 5 + 6x + x2 + -5 + -6x + -1x2 Reorder the terms: -14 + -6x + -1x2 = 5 + -5 + 6x + -6x + x2 + -1x2 Combine like terms: 5 + -5 = 0 -14 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 -14 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 -14 + -6x + -1x2 = 0 + x2 + -1x2 -14 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -14 + -6x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(14 + 6x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(14 + 6x + x2)' equal to zero and attempt to solve: Simplifying 14 + 6x + x2 = 0 Solving 14 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 6x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 6x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 6x + x2 = 0 + -14 6x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 6x + x2 = -14 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -14 + 9 Reorder the terms: 9 + 6x + x2 = -14 + 9 Combine like terms: -14 + 9 = -5 9 + 6x + x2 = -5 Factor a perfect square on the left side: (x + 3)(x + 3) = -5 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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