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Simplifying 26x2 + 26x + 324 = 0 Reorder the terms: 324 + 26x + 26x2 = 0 Solving 324 + 26x + 26x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(162 + 13x + 13x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(162 + 13x + 13x2)' equal to zero and attempt to solve: Simplifying 162 + 13x + 13x2 = 0 Solving 162 + 13x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 12.46153846 + x + x2 = 0 Move the constant term to the right: Add '-12.46153846' to each side of the equation. 12.46153846 + x + -12.46153846 + x2 = 0 + -12.46153846 Reorder the terms: 12.46153846 + -12.46153846 + x + x2 = 0 + -12.46153846 Combine like terms: 12.46153846 + -12.46153846 = 0.00000000 0.00000000 + x + x2 = 0 + -12.46153846 x + x2 = 0 + -12.46153846 Combine like terms: 0 + -12.46153846 = -12.46153846 x + x2 = -12.46153846 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. + 0.25 + x2 = -12.46153846 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -12.46153846 + 0.25 Combine like terms: -12.46153846 + 0.25 = -12.21153846 1.25 + x2 = -12.21153846 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -12.21153846 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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