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Simplifying y2 + 10y + 10 = 0 Reorder the terms: 10 + 10y + y2 = 0 Solving 10 + 10y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 10y + -10 + y2 = 0 + -10 Reorder the terms: 10 + -10 + 10y + y2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 10y + y2 = 0 + -10 10y + y2 = 0 + -10 Combine like terms: 0 + -10 = -10 10y + y2 = -10 The y term is 10y. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10y + 25 + y2 = -10 + 25 Reorder the terms: 25 + 10y + y2 = -10 + 25 Combine like terms: -10 + 25 = 15 25 + 10y + y2 = 15 Factor a perfect square on the left side: (y + 5)(y + 5) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (y + 5) equal to 3.872983346 and -3.872983346.Subproblem 1
y + 5 = 3.872983346 Simplifying y + 5 = 3.872983346 Reorder the terms: 5 + y = 3.872983346 Solving 5 + y = 3.872983346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 3.872983346 + -5 Combine like terms: 5 + -5 = 0 0 + y = 3.872983346 + -5 y = 3.872983346 + -5 Combine like terms: 3.872983346 + -5 = -1.127016654 y = -1.127016654 Simplifying y = -1.127016654Subproblem 2
y + 5 = -3.872983346 Simplifying y + 5 = -3.872983346 Reorder the terms: 5 + y = -3.872983346 Solving 5 + y = -3.872983346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = -3.872983346 + -5 Combine like terms: 5 + -5 = 0 0 + y = -3.872983346 + -5 y = -3.872983346 + -5 Combine like terms: -3.872983346 + -5 = -8.872983346 y = -8.872983346 Simplifying y = -8.872983346Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.127016654, -8.872983346}
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