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Simplifying y2 + 19 = 12y Reorder the terms: 19 + y2 = 12y Solving 19 + y2 = 12y Solving for variable 'y'. Reorder the terms: 19 + -12y + y2 = 12y + -12y Combine like terms: 12y + -12y = 0 19 + -12y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -12y + -19 + y2 = 0 + -19 Reorder the terms: 19 + -19 + -12y + y2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -12y + y2 = 0 + -19 -12y + y2 = 0 + -19 Combine like terms: 0 + -19 = -19 -12y + y2 = -19 The y term is -12y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y + 36 + y2 = -19 + 36 Reorder the terms: 36 + -12y + y2 = -19 + 36 Combine like terms: -19 + 36 = 17 36 + -12y + y2 = 17 Factor a perfect square on the left side: (y + -6)(y + -6) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (y + -6) equal to 4.123105626 and -4.123105626.Subproblem 1
y + -6 = 4.123105626 Simplifying y + -6 = 4.123105626 Reorder the terms: -6 + y = 4.123105626 Solving -6 + y = 4.123105626 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 4.123105626 + 6 Combine like terms: -6 + 6 = 0 0 + y = 4.123105626 + 6 y = 4.123105626 + 6 Combine like terms: 4.123105626 + 6 = 10.123105626 y = 10.123105626 Simplifying y = 10.123105626Subproblem 2
y + -6 = -4.123105626 Simplifying y + -6 = -4.123105626 Reorder the terms: -6 + y = -4.123105626 Solving -6 + y = -4.123105626 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -4.123105626 + 6 Combine like terms: -6 + 6 = 0 0 + y = -4.123105626 + 6 y = -4.123105626 + 6 Combine like terms: -4.123105626 + 6 = 1.876894374 y = 1.876894374 Simplifying y = 1.876894374Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.123105626, 1.876894374}
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