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Simplifying 7(2y2 + -6y + 2) + -4(3y2 + -2y + 6) = 0 Reorder the terms: 7(2 + -6y + 2y2) + -4(3y2 + -2y + 6) = 0 (2 * 7 + -6y * 7 + 2y2 * 7) + -4(3y2 + -2y + 6) = 0 (14 + -42y + 14y2) + -4(3y2 + -2y + 6) = 0 Reorder the terms: 14 + -42y + 14y2 + -4(6 + -2y + 3y2) = 0 14 + -42y + 14y2 + (6 * -4 + -2y * -4 + 3y2 * -4) = 0 14 + -42y + 14y2 + (-24 + 8y + -12y2) = 0 Reorder the terms: 14 + -24 + -42y + 8y + 14y2 + -12y2 = 0 Combine like terms: 14 + -24 = -10 -10 + -42y + 8y + 14y2 + -12y2 = 0 Combine like terms: -42y + 8y = -34y -10 + -34y + 14y2 + -12y2 = 0 Combine like terms: 14y2 + -12y2 = 2y2 -10 + -34y + 2y2 = 0 Solving -10 + -34y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -17y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -17y + y2)' equal to zero and attempt to solve: Simplifying -5 + -17y + y2 = 0 Solving -5 + -17y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -17y + 5 + y2 = 0 + 5 Reorder the terms: -5 + 5 + -17y + y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -17y + y2 = 0 + 5 -17y + y2 = 0 + 5 Combine like terms: 0 + 5 = 5 -17y + y2 = 5 The y term is -17y. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17y + 72.25 + y2 = 5 + 72.25 Reorder the terms: 72.25 + -17y + y2 = 5 + 72.25 Combine like terms: 5 + 72.25 = 77.25 72.25 + -17y + y2 = 77.25 Factor a perfect square on the left side: (y + -8.5)(y + -8.5) = 77.25 Calculate the square root of the right side: 8.789197916 Break this problem into two subproblems by setting (y + -8.5) equal to 8.789197916 and -8.789197916.Subproblem 1
y + -8.5 = 8.789197916 Simplifying y + -8.5 = 8.789197916 Reorder the terms: -8.5 + y = 8.789197916 Solving -8.5 + y = 8.789197916 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + y = 8.789197916 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + y = 8.789197916 + 8.5 y = 8.789197916 + 8.5 Combine like terms: 8.789197916 + 8.5 = 17.289197916 y = 17.289197916 Simplifying y = 17.289197916Subproblem 2
y + -8.5 = -8.789197916 Simplifying y + -8.5 = -8.789197916 Reorder the terms: -8.5 + y = -8.789197916 Solving -8.5 + y = -8.789197916 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + y = -8.789197916 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + y = -8.789197916 + 8.5 y = -8.789197916 + 8.5 Combine like terms: -8.789197916 + 8.5 = -0.289197916 y = -0.289197916 Simplifying y = -0.289197916Solution
The solution to the problem is based on the solutions from the subproblems. y = {17.289197916, -0.289197916}Solution
y = {17.289197916, -0.289197916}
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