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Simplifying (y2 + 4) = 2y2 + -1y + -10 Reorder the terms: (4 + y2) = 2y2 + -1y + -10 Remove parenthesis around (4 + y2) 4 + y2 = 2y2 + -1y + -10 Reorder the terms: 4 + y2 = -10 + -1y + 2y2 Solving 4 + y2 = -10 + -1y + 2y2 Solving for variable 'y'. Reorder the terms: 4 + 10 + y + y2 + -2y2 = -10 + -1y + 2y2 + 10 + y + -2y2 Combine like terms: 4 + 10 = 14 14 + y + y2 + -2y2 = -10 + -1y + 2y2 + 10 + y + -2y2 Combine like terms: y2 + -2y2 = -1y2 14 + y + -1y2 = -10 + -1y + 2y2 + 10 + y + -2y2 Reorder the terms: 14 + y + -1y2 = -10 + 10 + -1y + y + 2y2 + -2y2 Combine like terms: -10 + 10 = 0 14 + y + -1y2 = 0 + -1y + y + 2y2 + -2y2 14 + y + -1y2 = -1y + y + 2y2 + -2y2 Combine like terms: -1y + y = 0 14 + y + -1y2 = 0 + 2y2 + -2y2 14 + y + -1y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 14 + y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + -1y + y2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -1y + 14 + y2 = 0 + 14 Reorder the terms: -14 + 14 + -1y + y2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1y + y2 = 0 + 14 -1y + y2 = 0 + 14 Combine like terms: 0 + 14 = 14 -1y + y2 = 14 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 14 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 14 + 0.25 Combine like terms: 14 + 0.25 = 14.25 0.25 + -1y + y2 = 14.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (y + 0.5) equal to 3.774917218 and -3.774917218.Subproblem 1
y + 0.5 = 3.774917218 Simplifying y + 0.5 = 3.774917218 Reorder the terms: 0.5 + y = 3.774917218 Solving 0.5 + y = 3.774917218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 3.774917218 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 3.774917218 + -0.5 y = 3.774917218 + -0.5 Combine like terms: 3.774917218 + -0.5 = 3.274917218 y = 3.274917218 Simplifying y = 3.274917218Subproblem 2
y + 0.5 = -3.774917218 Simplifying y + 0.5 = -3.774917218 Reorder the terms: 0.5 + y = -3.774917218 Solving 0.5 + y = -3.774917218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -3.774917218 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -3.774917218 + -0.5 y = -3.774917218 + -0.5 Combine like terms: -3.774917218 + -0.5 = -4.274917218 y = -4.274917218 Simplifying y = -4.274917218Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.274917218, -4.274917218}
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