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Simplifying 0 = x * x + 6x + 11 Multiply x * x 0 = x2 + 6x + 11 Reorder the terms: 0 = 11 + 6x + x2 Solving 0 = 11 + 6x + x2 Solving for variable 'x'. Combine like terms: 0 + -11 = -11 -11 + -6x + -1x2 = 11 + 6x + x2 + -11 + -6x + -1x2 Reorder the terms: -11 + -6x + -1x2 = 11 + -11 + 6x + -6x + x2 + -1x2 Combine like terms: 11 + -11 = 0 -11 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 -11 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 -11 + -6x + -1x2 = 0 + x2 + -1x2 -11 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -11 + -6x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 6x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 6x + x2)' equal to zero and attempt to solve: Simplifying 11 + 6x + x2 = 0 Solving 11 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 6x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 6x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 6x + x2 = 0 + -11 6x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 6x + x2 = -11 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 = -11 + 9 Reorder the terms: 9 + 6x + x2 = -11 + 9 Combine like terms: -11 + 9 = -2 9 + 6x + x2 = -2 Factor a perfect square on the left side: (x + 3)(x + 3) = -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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