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Simplifying y2 + 21y = 19 Reorder the terms: 21y + y2 = 19 Solving 21y + y2 = 19 Solving for variable 'y'. Reorder the terms: -19 + 21y + y2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 21y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 21y + 19 + y2 = 0 + 19 Reorder the terms: -19 + 19 + 21y + y2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 21y + y2 = 0 + 19 21y + y2 = 0 + 19 Combine like terms: 0 + 19 = 19 21y + y2 = 19 The y term is 21y. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21y + 110.25 + y2 = 19 + 110.25 Reorder the terms: 110.25 + 21y + y2 = 19 + 110.25 Combine like terms: 19 + 110.25 = 129.25 110.25 + 21y + y2 = 129.25 Factor a perfect square on the left side: (y + 10.5)(y + 10.5) = 129.25 Calculate the square root of the right side: 11.368817001 Break this problem into two subproblems by setting (y + 10.5) equal to 11.368817001 and -11.368817001.Subproblem 1
y + 10.5 = 11.368817001 Simplifying y + 10.5 = 11.368817001 Reorder the terms: 10.5 + y = 11.368817001 Solving 10.5 + y = 11.368817001 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + y = 11.368817001 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + y = 11.368817001 + -10.5 y = 11.368817001 + -10.5 Combine like terms: 11.368817001 + -10.5 = 0.868817001 y = 0.868817001 Simplifying y = 0.868817001Subproblem 2
y + 10.5 = -11.368817001 Simplifying y + 10.5 = -11.368817001 Reorder the terms: 10.5 + y = -11.368817001 Solving 10.5 + y = -11.368817001 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + y = -11.368817001 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + y = -11.368817001 + -10.5 y = -11.368817001 + -10.5 Combine like terms: -11.368817001 + -10.5 = -21.868817001 y = -21.868817001 Simplifying y = -21.868817001Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.868817001, -21.868817001}
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