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Simplifying 4y + -10 = y(y) + -62 Reorder the terms: -10 + 4y = y(y) + -62 Multiply y * y -10 + 4y = y2 + -62 Reorder the terms: -10 + 4y = -62 + y2 Solving -10 + 4y = -62 + y2 Solving for variable 'y'. Reorder the terms: -10 + 62 + 4y + -1y2 = -62 + y2 + 62 + -1y2 Combine like terms: -10 + 62 = 52 52 + 4y + -1y2 = -62 + y2 + 62 + -1y2 Reorder the terms: 52 + 4y + -1y2 = -62 + 62 + y2 + -1y2 Combine like terms: -62 + 62 = 0 52 + 4y + -1y2 = 0 + y2 + -1y2 52 + 4y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 52 + 4y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -52 + -4y + y2 = 0 Move the constant term to the right: Add '52' to each side of the equation. -52 + -4y + 52 + y2 = 0 + 52 Reorder the terms: -52 + 52 + -4y + y2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -4y + y2 = 0 + 52 -4y + y2 = 0 + 52 Combine like terms: 0 + 52 = 52 -4y + y2 = 52 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 52 + 4 Reorder the terms: 4 + -4y + y2 = 52 + 4 Combine like terms: 52 + 4 = 56 4 + -4y + y2 = 56 Factor a perfect square on the left side: (y + -2)(y + -2) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (y + -2) equal to 7.483314774 and -7.483314774.Subproblem 1
y + -2 = 7.483314774 Simplifying y + -2 = 7.483314774 Reorder the terms: -2 + y = 7.483314774 Solving -2 + y = 7.483314774 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 7.483314774 + 2 Combine like terms: -2 + 2 = 0 0 + y = 7.483314774 + 2 y = 7.483314774 + 2 Combine like terms: 7.483314774 + 2 = 9.483314774 y = 9.483314774 Simplifying y = 9.483314774Subproblem 2
y + -2 = -7.483314774 Simplifying y + -2 = -7.483314774 Reorder the terms: -2 + y = -7.483314774 Solving -2 + y = -7.483314774 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -7.483314774 + 2 Combine like terms: -2 + 2 = 0 0 + y = -7.483314774 + 2 y = -7.483314774 + 2 Combine like terms: -7.483314774 + 2 = -5.483314774 y = -5.483314774 Simplifying y = -5.483314774Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.483314774, -5.483314774}
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