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Simplifying y2 + -3y = 2(2y + -4) Reorder the terms: -3y + y2 = 2(2y + -4) Reorder the terms: -3y + y2 = 2(-4 + 2y) -3y + y2 = (-4 * 2 + 2y * 2) -3y + y2 = (-8 + 4y) Solving -3y + y2 = -8 + 4y Solving for variable 'y'. Reorder the terms: 8 + -3y + -4y + y2 = -8 + 4y + 8 + -4y Combine like terms: -3y + -4y = -7y 8 + -7y + y2 = -8 + 4y + 8 + -4y Reorder the terms: 8 + -7y + y2 = -8 + 8 + 4y + -4y Combine like terms: -8 + 8 = 0 8 + -7y + y2 = 0 + 4y + -4y 8 + -7y + y2 = 4y + -4y Combine like terms: 4y + -4y = 0 8 + -7y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -7y + -8 + y2 = 0 + -8 Reorder the terms: 8 + -8 + -7y + y2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7y + y2 = 0 + -8 -7y + y2 = 0 + -8 Combine like terms: 0 + -8 = -8 -7y + y2 = -8 The y term is -7y. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7y + 12.25 + y2 = -8 + 12.25 Reorder the terms: 12.25 + -7y + y2 = -8 + 12.25 Combine like terms: -8 + 12.25 = 4.25 12.25 + -7y + y2 = 4.25 Factor a perfect square on the left side: (y + -3.5)(y + -3.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (y + -3.5) equal to 2.061552813 and -2.061552813.Subproblem 1
y + -3.5 = 2.061552813 Simplifying y + -3.5 = 2.061552813 Reorder the terms: -3.5 + y = 2.061552813 Solving -3.5 + y = 2.061552813 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = 2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = 2.061552813 + 3.5 y = 2.061552813 + 3.5 Combine like terms: 2.061552813 + 3.5 = 5.561552813 y = 5.561552813 Simplifying y = 5.561552813Subproblem 2
y + -3.5 = -2.061552813 Simplifying y + -3.5 = -2.061552813 Reorder the terms: -3.5 + y = -2.061552813 Solving -3.5 + y = -2.061552813 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = -2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = -2.061552813 + 3.5 y = -2.061552813 + 3.5 Combine like terms: -2.061552813 + 3.5 = 1.438447187 y = 1.438447187 Simplifying y = 1.438447187Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.561552813, 1.438447187}
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