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Simplifying 7y2 + -13y = 25 Reorder the terms: -13y + 7y2 = 25 Solving -13y + 7y2 = 25 Solving for variable 'y'. Reorder the terms: -25 + -13y + 7y2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -13y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.571428571 + -1.857142857y + y2 = 0 Move the constant term to the right: Add '3.571428571' to each side of the equation. -3.571428571 + -1.857142857y + 3.571428571 + y2 = 0 + 3.571428571 Reorder the terms: -3.571428571 + 3.571428571 + -1.857142857y + y2 = 0 + 3.571428571 Combine like terms: -3.571428571 + 3.571428571 = 0.000000000 0.000000000 + -1.857142857y + y2 = 0 + 3.571428571 -1.857142857y + y2 = 0 + 3.571428571 Combine like terms: 0 + 3.571428571 = 3.571428571 -1.857142857y + y2 = 3.571428571 The y term is -1.857142857y. Take half its coefficient (-0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. -1.857142857y + 0.8622448978 + y2 = 3.571428571 + 0.8622448978 Reorder the terms: 0.8622448978 + -1.857142857y + y2 = 3.571428571 + 0.8622448978 Combine like terms: 3.571428571 + 0.8622448978 = 4.4336734688 0.8622448978 + -1.857142857y + y2 = 4.4336734688 Factor a perfect square on the left side: (y + -0.9285714285)(y + -0.9285714285) = 4.4336734688 Calculate the square root of the right side: 2.105628996 Break this problem into two subproblems by setting (y + -0.9285714285) equal to 2.105628996 and -2.105628996.Subproblem 1
y + -0.9285714285 = 2.105628996 Simplifying y + -0.9285714285 = 2.105628996 Reorder the terms: -0.9285714285 + y = 2.105628996 Solving -0.9285714285 + y = 2.105628996 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + y = 2.105628996 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + y = 2.105628996 + 0.9285714285 y = 2.105628996 + 0.9285714285 Combine like terms: 2.105628996 + 0.9285714285 = 3.0342004245 y = 3.0342004245 Simplifying y = 3.0342004245Subproblem 2
y + -0.9285714285 = -2.105628996 Simplifying y + -0.9285714285 = -2.105628996 Reorder the terms: -0.9285714285 + y = -2.105628996 Solving -0.9285714285 + y = -2.105628996 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + y = -2.105628996 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + y = -2.105628996 + 0.9285714285 y = -2.105628996 + 0.9285714285 Combine like terms: -2.105628996 + 0.9285714285 = -1.1770575675 y = -1.1770575675 Simplifying y = -1.1770575675Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.0342004245, -1.1770575675}
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