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Simplifying 5y2 + -10 = 13y + 4 Reorder the terms: -10 + 5y2 = 13y + 4 Reorder the terms: -10 + 5y2 = 4 + 13y Solving -10 + 5y2 = 4 + 13y Solving for variable 'y'. Reorder the terms: -10 + -4 + -13y + 5y2 = 4 + 13y + -4 + -13y Combine like terms: -10 + -4 = -14 -14 + -13y + 5y2 = 4 + 13y + -4 + -13y Reorder the terms: -14 + -13y + 5y2 = 4 + -4 + 13y + -13y Combine like terms: 4 + -4 = 0 -14 + -13y + 5y2 = 0 + 13y + -13y -14 + -13y + 5y2 = 13y + -13y Combine like terms: 13y + -13y = 0 -14 + -13y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + -2.6y + y2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -2.6y + 2.8 + y2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + -2.6y + y2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -2.6y + y2 = 0 + 2.8 -2.6y + y2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 -2.6y + y2 = 2.8 The y term is -2.6y. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6y + 1.69 + y2 = 2.8 + 1.69 Reorder the terms: 1.69 + -2.6y + y2 = 2.8 + 1.69 Combine like terms: 2.8 + 1.69 = 4.49 1.69 + -2.6y + y2 = 4.49 Factor a perfect square on the left side: (y + -1.3)(y + -1.3) = 4.49 Calculate the square root of the right side: 2.11896201 Break this problem into two subproblems by setting (y + -1.3) equal to 2.11896201 and -2.11896201.Subproblem 1
y + -1.3 = 2.11896201 Simplifying y + -1.3 = 2.11896201 Reorder the terms: -1.3 + y = 2.11896201 Solving -1.3 + y = 2.11896201 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + y = 2.11896201 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + y = 2.11896201 + 1.3 y = 2.11896201 + 1.3 Combine like terms: 2.11896201 + 1.3 = 3.41896201 y = 3.41896201 Simplifying y = 3.41896201Subproblem 2
y + -1.3 = -2.11896201 Simplifying y + -1.3 = -2.11896201 Reorder the terms: -1.3 + y = -2.11896201 Solving -1.3 + y = -2.11896201 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + y = -2.11896201 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + y = -2.11896201 + 1.3 y = -2.11896201 + 1.3 Combine like terms: -2.11896201 + 1.3 = -0.81896201 y = -0.81896201 Simplifying y = -0.81896201Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.41896201, -0.81896201}
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