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Simplifying x2 + x2 + 22x + 154 = 0 Reorder the terms: 154 + 22x + x2 + x2 = 0 Combine like terms: x2 + x2 = 2x2 154 + 22x + 2x2 = 0 Solving 154 + 22x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(77 + 11x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(77 + 11x + x2)' equal to zero and attempt to solve: Simplifying 77 + 11x + x2 = 0 Solving 77 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-77' to each side of the equation. 77 + 11x + -77 + x2 = 0 + -77 Reorder the terms: 77 + -77 + 11x + x2 = 0 + -77 Combine like terms: 77 + -77 = 0 0 + 11x + x2 = 0 + -77 11x + x2 = 0 + -77 Combine like terms: 0 + -77 = -77 11x + x2 = -77 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = -77 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -77 + 30.25 Combine like terms: -77 + 30.25 = -46.75 30.25 + 11x + x2 = -46.75 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = -46.75 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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