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Simplifying 8y2 + -8y + 12 + -12y2 + -8y + 6 = 0 Reorder the terms: 12 + 6 + -8y + -8y + 8y2 + -12y2 = 0 Combine like terms: 12 + 6 = 18 18 + -8y + -8y + 8y2 + -12y2 = 0 Combine like terms: -8y + -8y = -16y 18 + -16y + 8y2 + -12y2 = 0 Combine like terms: 8y2 + -12y2 = -4y2 18 + -16y + -4y2 = 0 Solving 18 + -16y + -4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -8y + -2y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -8y + -2y2)' equal to zero and attempt to solve: Simplifying 9 + -8y + -2y2 = 0 Solving 9 + -8y + -2y2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4.5 + 4y + y2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 4y + 4.5 + y2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 4y + y2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 4y + y2 = 0 + 4.5 4y + y2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 4y + y2 = 4.5 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = 4.5 + 4 Reorder the terms: 4 + 4y + y2 = 4.5 + 4 Combine like terms: 4.5 + 4 = 8.5 4 + 4y + y2 = 8.5 Factor a perfect square on the left side: (y + 2)(y + 2) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (y + 2) equal to 2.915475947 and -2.915475947.Subproblem 1
y + 2 = 2.915475947 Simplifying y + 2 = 2.915475947 Reorder the terms: 2 + y = 2.915475947 Solving 2 + y = 2.915475947 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 2.915475947 + -2 Combine like terms: 2 + -2 = 0 0 + y = 2.915475947 + -2 y = 2.915475947 + -2 Combine like terms: 2.915475947 + -2 = 0.915475947 y = 0.915475947 Simplifying y = 0.915475947Subproblem 2
y + 2 = -2.915475947 Simplifying y + 2 = -2.915475947 Reorder the terms: 2 + y = -2.915475947 Solving 2 + y = -2.915475947 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -2.915475947 + -2 Combine like terms: 2 + -2 = 0 0 + y = -2.915475947 + -2 y = -2.915475947 + -2 Combine like terms: -2.915475947 + -2 = -4.915475947 y = -4.915475947 Simplifying y = -4.915475947Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.915475947, -4.915475947}Solution
y = {0.915475947, -4.915475947}
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