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Simplifying y2 + -6y = 10 Reorder the terms: -6y + y2 = 10 Solving -6y + y2 = 10 Solving for variable 'y'. Reorder the terms: -10 + -6y + y2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -6y + 10 + y2 = 0 + 10 Reorder the terms: -10 + 10 + -6y + y2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -6y + y2 = 0 + 10 -6y + y2 = 0 + 10 Combine like terms: 0 + 10 = 10 -6y + y2 = 10 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = 10 + 9 Reorder the terms: 9 + -6y + y2 = 10 + 9 Combine like terms: 10 + 9 = 19 9 + -6y + y2 = 19 Factor a perfect square on the left side: (y + -3)(y + -3) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (y + -3) equal to 4.358898944 and -4.358898944.Subproblem 1
y + -3 = 4.358898944 Simplifying y + -3 = 4.358898944 Reorder the terms: -3 + y = 4.358898944 Solving -3 + y = 4.358898944 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 4.358898944 + 3 Combine like terms: -3 + 3 = 0 0 + y = 4.358898944 + 3 y = 4.358898944 + 3 Combine like terms: 4.358898944 + 3 = 7.358898944 y = 7.358898944 Simplifying y = 7.358898944Subproblem 2
y + -3 = -4.358898944 Simplifying y + -3 = -4.358898944 Reorder the terms: -3 + y = -4.358898944 Solving -3 + y = -4.358898944 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -4.358898944 + 3 Combine like terms: -3 + 3 = 0 0 + y = -4.358898944 + 3 y = -4.358898944 + 3 Combine like terms: -4.358898944 + 3 = -1.358898944 y = -1.358898944 Simplifying y = -1.358898944Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.358898944, -1.358898944}
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