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Simplifying (x + 26)(x + 26) + x2 = 220 Reorder the terms: (26 + x)(x + 26) + x2 = 220 Reorder the terms: (26 + x)(26 + x) + x2 = 220 Multiply (26 + x) * (26 + x) (26(26 + x) + x(26 + x)) + x2 = 220 ((26 * 26 + x * 26) + x(26 + x)) + x2 = 220 ((676 + 26x) + x(26 + x)) + x2 = 220 (676 + 26x + (26 * x + x * x)) + x2 = 220 (676 + 26x + (26x + x2)) + x2 = 220 Combine like terms: 26x + 26x = 52x (676 + 52x + x2) + x2 = 220 Combine like terms: x2 + x2 = 2x2 676 + 52x + 2x2 = 220 Solving 676 + 52x + 2x2 = 220 Solving for variable 'x'. Reorder the terms: 676 + -220 + 52x + 2x2 = 220 + -220 Combine like terms: 676 + -220 = 456 456 + 52x + 2x2 = 220 + -220 Combine like terms: 220 + -220 = 0 456 + 52x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(228 + 26x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(228 + 26x + x2)' equal to zero and attempt to solve: Simplifying 228 + 26x + x2 = 0 Solving 228 + 26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-228' to each side of the equation. 228 + 26x + -228 + x2 = 0 + -228 Reorder the terms: 228 + -228 + 26x + x2 = 0 + -228 Combine like terms: 228 + -228 = 0 0 + 26x + x2 = 0 + -228 26x + x2 = 0 + -228 Combine like terms: 0 + -228 = -228 26x + x2 = -228 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = -228 + 169 Reorder the terms: 169 + 26x + x2 = -228 + 169 Combine like terms: -228 + 169 = -59 169 + 26x + x2 = -59 Factor a perfect square on the left side: (x + 13)(x + 13) = -59 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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