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Simplifying y2 + -11y + -3y + 28 = 0 Reorder the terms: 28 + -11y + -3y + y2 = 0 Combine like terms: -11y + -3y = -14y 28 + -14y + y2 = 0 Solving 28 + -14y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -14y + -28 + y2 = 0 + -28 Reorder the terms: 28 + -28 + -14y + y2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -14y + y2 = 0 + -28 -14y + y2 = 0 + -28 Combine like terms: 0 + -28 = -28 -14y + y2 = -28 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 = -28 + 49 Reorder the terms: 49 + -14y + y2 = -28 + 49 Combine like terms: -28 + 49 = 21 49 + -14y + y2 = 21 Factor a perfect square on the left side: (y + -7)(y + -7) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (y + -7) equal to 4.582575695 and -4.582575695.Subproblem 1
y + -7 = 4.582575695 Simplifying y + -7 = 4.582575695 Reorder the terms: -7 + y = 4.582575695 Solving -7 + y = 4.582575695 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 = 4.582575695 + 7 Combine like terms: -7 + 7 = 0 0 + y = 4.582575695 + 7 y = 4.582575695 + 7 Combine like terms: 4.582575695 + 7 = 11.582575695 y = 11.582575695 Simplifying y = 11.582575695Subproblem 2
y + -7 = -4.582575695 Simplifying y + -7 = -4.582575695 Reorder the terms: -7 + y = -4.582575695 Solving -7 + y = -4.582575695 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 = -4.582575695 + 7 Combine like terms: -7 + 7 = 0 0 + y = -4.582575695 + 7 y = -4.582575695 + 7 Combine like terms: -4.582575695 + 7 = 2.417424305 y = 2.417424305 Simplifying y = 2.417424305Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.582575695, 2.417424305}
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