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Simplifying 13y2 + -6y + -20 = 0 Reorder the terms: -20 + -6y + 13y2 = 0 Solving -20 + -6y + 13y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -1.538461538 + -0.4615384615y + y2 = 0 Move the constant term to the right: Add '1.538461538' to each side of the equation. -1.538461538 + -0.4615384615y + 1.538461538 + y2 = 0 + 1.538461538 Reorder the terms: -1.538461538 + 1.538461538 + -0.4615384615y + y2 = 0 + 1.538461538 Combine like terms: -1.538461538 + 1.538461538 = 0.000000000 0.000000000 + -0.4615384615y + y2 = 0 + 1.538461538 -0.4615384615y + y2 = 0 + 1.538461538 Combine like terms: 0 + 1.538461538 = 1.538461538 -0.4615384615y + y2 = 1.538461538 The y term is -0.4615384615y. Take half its coefficient (-0.2307692308). Square it (0.05325443788) and add it to both sides. Add '0.05325443788' to each side of the equation. -0.4615384615y + 0.05325443788 + y2 = 1.538461538 + 0.05325443788 Reorder the terms: 0.05325443788 + -0.4615384615y + y2 = 1.538461538 + 0.05325443788 Combine like terms: 1.538461538 + 0.05325443788 = 1.59171597588 0.05325443788 + -0.4615384615y + y2 = 1.59171597588 Factor a perfect square on the left side: (y + -0.2307692308)(y + -0.2307692308) = 1.59171597588 Calculate the square root of the right side: 1.261632267 Break this problem into two subproblems by setting (y + -0.2307692308) equal to 1.261632267 and -1.261632267.Subproblem 1
y + -0.2307692308 = 1.261632267 Simplifying y + -0.2307692308 = 1.261632267 Reorder the terms: -0.2307692308 + y = 1.261632267 Solving -0.2307692308 + y = 1.261632267 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2307692308' to each side of the equation. -0.2307692308 + 0.2307692308 + y = 1.261632267 + 0.2307692308 Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000 0.0000000000 + y = 1.261632267 + 0.2307692308 y = 1.261632267 + 0.2307692308 Combine like terms: 1.261632267 + 0.2307692308 = 1.4924014978 y = 1.4924014978 Simplifying y = 1.4924014978Subproblem 2
y + -0.2307692308 = -1.261632267 Simplifying y + -0.2307692308 = -1.261632267 Reorder the terms: -0.2307692308 + y = -1.261632267 Solving -0.2307692308 + y = -1.261632267 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2307692308' to each side of the equation. -0.2307692308 + 0.2307692308 + y = -1.261632267 + 0.2307692308 Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000 0.0000000000 + y = -1.261632267 + 0.2307692308 y = -1.261632267 + 0.2307692308 Combine like terms: -1.261632267 + 0.2307692308 = -1.0308630362 y = -1.0308630362 Simplifying y = -1.0308630362Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.4924014978, -1.0308630362}
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