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Simplifying y2 + 4y = 12.9 Reorder the terms: 4y + y2 = 12.9 Solving 4y + y2 = 12.9 Solving for variable 'y'. Reorder the terms: -12.9 + 4y + y2 = 12.9 + -12.9 Combine like terms: 12.9 + -12.9 = 0.0 -12.9 + 4y + y2 = 0.0 Begin completing the square. Move the constant term to the right: Add '12.9' to each side of the equation. -12.9 + 4y + 12.9 + y2 = 0.0 + 12.9 Reorder the terms: -12.9 + 12.9 + 4y + y2 = 0.0 + 12.9 Combine like terms: -12.9 + 12.9 = 0.0 0.0 + 4y + y2 = 0.0 + 12.9 4y + y2 = 0.0 + 12.9 Combine like terms: 0.0 + 12.9 = 12.9 4y + y2 = 12.9 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = 12.9 + 4 Reorder the terms: 4 + 4y + y2 = 12.9 + 4 Combine like terms: 12.9 + 4 = 16.9 4 + 4y + y2 = 16.9 Factor a perfect square on the left side: (y + 2)(y + 2) = 16.9 Calculate the square root of the right side: 4.110960958 Break this problem into two subproblems by setting (y + 2) equal to 4.110960958 and -4.110960958.Subproblem 1
y + 2 = 4.110960958 Simplifying y + 2 = 4.110960958 Reorder the terms: 2 + y = 4.110960958 Solving 2 + y = 4.110960958 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 4.110960958 + -2 Combine like terms: 2 + -2 = 0 0 + y = 4.110960958 + -2 y = 4.110960958 + -2 Combine like terms: 4.110960958 + -2 = 2.110960958 y = 2.110960958 Simplifying y = 2.110960958Subproblem 2
y + 2 = -4.110960958 Simplifying y + 2 = -4.110960958 Reorder the terms: 2 + y = -4.110960958 Solving 2 + y = -4.110960958 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -4.110960958 + -2 Combine like terms: 2 + -2 = 0 0 + y = -4.110960958 + -2 y = -4.110960958 + -2 Combine like terms: -4.110960958 + -2 = -6.110960958 y = -6.110960958 Simplifying y = -6.110960958Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.110960958, -6.110960958}
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