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Simplifying 14y + -1y2 = 25 Solving 14y + -1y2 = 25 Solving for variable 'y'. Reorder the terms: -25 + 14y + -1y2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 14y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 25 + -14y + y2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -14y + -25 + y2 = 0 + -25 Reorder the terms: 25 + -25 + -14y + y2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -14y + y2 = 0 + -25 -14y + y2 = 0 + -25 Combine like terms: 0 + -25 = -25 -14y + y2 = -25 The y term is -14y. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14y + 49 + y2 = -25 + 49 Reorder the terms: 49 + -14y + y2 = -25 + 49 Combine like terms: -25 + 49 = 24 49 + -14y + y2 = 24 Factor a perfect square on the left side: (y + -7)(y + -7) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (y + -7) equal to 4.898979486 and -4.898979486.Subproblem 1
y + -7 = 4.898979486 Simplifying y + -7 = 4.898979486 Reorder the terms: -7 + y = 4.898979486 Solving -7 + y = 4.898979486 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = 4.898979486 + 7 Combine like terms: -7 + 7 = 0 0 + y = 4.898979486 + 7 y = 4.898979486 + 7 Combine like terms: 4.898979486 + 7 = 11.898979486 y = 11.898979486 Simplifying y = 11.898979486Subproblem 2
y + -7 = -4.898979486 Simplifying y + -7 = -4.898979486 Reorder the terms: -7 + y = -4.898979486 Solving -7 + y = -4.898979486 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = -4.898979486 + 7 Combine like terms: -7 + 7 = 0 0 + y = -4.898979486 + 7 y = -4.898979486 + 7 Combine like terms: -4.898979486 + 7 = 2.101020514 y = 2.101020514 Simplifying y = 2.101020514Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.898979486, 2.101020514}
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