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Simplifying -1x2 + -1x = 11 Reorder the terms: -1x + -1x2 = 11 Solving -1x + -1x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -1x + -1x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -1x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + x + x2)' equal to zero and attempt to solve: Simplifying 11 + x + x2 = 0 Solving 11 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + x + x2 = 0 + -11 x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 x + x2 = -11 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = -11 + 0.25 Reorder the terms: 0.25 + x + x2 = -11 + 0.25 Combine like terms: -11 + 0.25 = -10.75 0.25 + x + x2 = -10.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -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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