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Simplifying y2 + 10y + 6 = 0 Reorder the terms: 6 + 10y + y2 = 0 Solving 6 + 10y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 10y + -6 + y2 = 0 + -6 Reorder the terms: 6 + -6 + 10y + y2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 10y + y2 = 0 + -6 10y + y2 = 0 + -6 Combine like terms: 0 + -6 = -6 10y + y2 = -6 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 = -6 + 25 Reorder the terms: 25 + 10y + y2 = -6 + 25 Combine like terms: -6 + 25 = 19 25 + 10y + y2 = 19 Factor a perfect square on the left side: (y + 5)(y + 5) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (y + 5) equal to 4.358898944 and -4.358898944.Subproblem 1
y + 5 = 4.358898944 Simplifying y + 5 = 4.358898944 Reorder the terms: 5 + y = 4.358898944 Solving 5 + y = 4.358898944 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 = 4.358898944 + -5 Combine like terms: 5 + -5 = 0 0 + y = 4.358898944 + -5 y = 4.358898944 + -5 Combine like terms: 4.358898944 + -5 = -0.641101056 y = -0.641101056 Simplifying y = -0.641101056Subproblem 2
y + 5 = -4.358898944 Simplifying y + 5 = -4.358898944 Reorder the terms: 5 + y = -4.358898944 Solving 5 + y = -4.358898944 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 = -4.358898944 + -5 Combine like terms: 5 + -5 = 0 0 + y = -4.358898944 + -5 y = -4.358898944 + -5 Combine like terms: -4.358898944 + -5 = -9.358898944 y = -9.358898944 Simplifying y = -9.358898944Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.641101056, -9.358898944}
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