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Simplifying y2 + -14y = -32 Reorder the terms: -14y + y2 = -32 Solving -14y + y2 = -32 Solving for variable 'y'. Reorder the terms: 32 + -14y + y2 = -32 + 32 Combine like terms: -32 + 32 = 0 32 + -14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -14y + -32 + y2 = 0 + -32 Reorder the terms: 32 + -32 + -14y + y2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -14y + y2 = 0 + -32 -14y + y2 = 0 + -32 Combine like terms: 0 + -32 = -32 -14y + y2 = -32 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 = -32 + 49 Reorder the terms: 49 + -14y + y2 = -32 + 49 Combine like terms: -32 + 49 = 17 49 + -14y + y2 = 17 Factor a perfect square on the left side: (y + -7)(y + -7) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (y + -7) equal to 4.123105626 and -4.123105626.Subproblem 1
y + -7 = 4.123105626 Simplifying y + -7 = 4.123105626 Reorder the terms: -7 + y = 4.123105626 Solving -7 + y = 4.123105626 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 = 4.123105626 + 7 Combine like terms: -7 + 7 = 0 0 + y = 4.123105626 + 7 y = 4.123105626 + 7 Combine like terms: 4.123105626 + 7 = 11.123105626 y = 11.123105626 Simplifying y = 11.123105626Subproblem 2
y + -7 = -4.123105626 Simplifying y + -7 = -4.123105626 Reorder the terms: -7 + y = -4.123105626 Solving -7 + y = -4.123105626 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 = -4.123105626 + 7 Combine like terms: -7 + 7 = 0 0 + y = -4.123105626 + 7 y = -4.123105626 + 7 Combine like terms: -4.123105626 + 7 = 2.876894374 y = 2.876894374 Simplifying y = 2.876894374Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.123105626, 2.876894374}
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