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Simplifying y2 + -14y + -13 = 7 Reorder the terms: -13 + -14y + y2 = 7 Solving -13 + -14y + y2 = 7 Solving for variable 'y'. Reorder the terms: -13 + -7 + -14y + y2 = 7 + -7 Combine like terms: -13 + -7 = -20 -20 + -14y + y2 = 7 + -7 Combine like terms: 7 + -7 = 0 -20 + -14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -14y + 20 + y2 = 0 + 20 Reorder the terms: -20 + 20 + -14y + y2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -14y + y2 = 0 + 20 -14y + y2 = 0 + 20 Combine like terms: 0 + 20 = 20 -14y + y2 = 20 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 = 20 + 49 Reorder the terms: 49 + -14y + y2 = 20 + 49 Combine like terms: 20 + 49 = 69 49 + -14y + y2 = 69 Factor a perfect square on the left side: (y + -7)(y + -7) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (y + -7) equal to 8.306623863 and -8.306623863.Subproblem 1
y + -7 = 8.306623863 Simplifying y + -7 = 8.306623863 Reorder the terms: -7 + y = 8.306623863 Solving -7 + y = 8.306623863 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 = 8.306623863 + 7 Combine like terms: -7 + 7 = 0 0 + y = 8.306623863 + 7 y = 8.306623863 + 7 Combine like terms: 8.306623863 + 7 = 15.306623863 y = 15.306623863 Simplifying y = 15.306623863Subproblem 2
y + -7 = -8.306623863 Simplifying y + -7 = -8.306623863 Reorder the terms: -7 + y = -8.306623863 Solving -7 + y = -8.306623863 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 = -8.306623863 + 7 Combine like terms: -7 + 7 = 0 0 + y = -8.306623863 + 7 y = -8.306623863 + 7 Combine like terms: -8.306623863 + 7 = -1.306623863 y = -1.306623863 Simplifying y = -1.306623863Solution
The solution to the problem is based on the solutions from the subproblems. y = {15.306623863, -1.306623863}
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