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Simplifying 25a2 + 5ab + 25b2 = 0 Reorder the terms: 5ab + 25a2 + 25b2 = 0 Solving 5ab + 25a2 + 25b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5'. 5(ab + 5a2 + 5b2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(ab + 5a2 + 5b2)' equal to zero and attempt to solve: Simplifying ab + 5a2 + 5b2 = 0 Solving ab + 5a2 + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2ab + a2 + b2 = 0 Move the constant term to the right: Add '-1b2' to each side of the equation. 0.2ab + a2 + b2 + -1b2 = 0 + -1b2 Combine like terms: b2 + -1b2 = 0 0.2ab + a2 + 0 = 0 + -1b2 0.2ab + a2 = 0 + -1b2 Remove the zero: 0.2ab + a2 = -1b2 The a term is ab. Take half its coefficient (0.5b). Square it (0.25b2) and add it to both sides. Add '0.25b2' to each side of the equation. 0.2ab + a2 + 0.25b2 = -1b2 + 0.25b2 Combine like terms: -1b2 + 0.25b2 = -0.75b2 0.2ab + a2 + 0.25b2 = -0.75b2 Factor a perfect square on the left side: (a + 0.5b)(a + 0.5b) = -0.75b2 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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