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Simplifying 2y(y + -8) = 3y + 18 Reorder the terms: 2y(-8 + y) = 3y + 18 (-8 * 2y + y * 2y) = 3y + 18 (-16y + 2y2) = 3y + 18 Reorder the terms: -16y + 2y2 = 18 + 3y Solving -16y + 2y2 = 18 + 3y Solving for variable 'y'. Reorder the terms: -18 + -16y + -3y + 2y2 = 18 + 3y + -18 + -3y Combine like terms: -16y + -3y = -19y -18 + -19y + 2y2 = 18 + 3y + -18 + -3y Reorder the terms: -18 + -19y + 2y2 = 18 + -18 + 3y + -3y Combine like terms: 18 + -18 = 0 -18 + -19y + 2y2 = 0 + 3y + -3y -18 + -19y + 2y2 = 3y + -3y Combine like terms: 3y + -3y = 0 -18 + -19y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9 + -9.5y + y2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -9.5y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + -9.5y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -9.5y + y2 = 0 + 9 -9.5y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 -9.5y + y2 = 9 The y term is -9.5y. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5y + 22.5625 + y2 = 9 + 22.5625 Reorder the terms: 22.5625 + -9.5y + y2 = 9 + 22.5625 Combine like terms: 9 + 22.5625 = 31.5625 22.5625 + -9.5y + y2 = 31.5625 Factor a perfect square on the left side: (y + -4.75)(y + -4.75) = 31.5625 Calculate the square root of the right side: 5.618051264 Break this problem into two subproblems by setting (y + -4.75) equal to 5.618051264 and -5.618051264.Subproblem 1
y + -4.75 = 5.618051264 Simplifying y + -4.75 = 5.618051264 Reorder the terms: -4.75 + y = 5.618051264 Solving -4.75 + y = 5.618051264 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + y = 5.618051264 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + y = 5.618051264 + 4.75 y = 5.618051264 + 4.75 Combine like terms: 5.618051264 + 4.75 = 10.368051264 y = 10.368051264 Simplifying y = 10.368051264Subproblem 2
y + -4.75 = -5.618051264 Simplifying y + -4.75 = -5.618051264 Reorder the terms: -4.75 + y = -5.618051264 Solving -4.75 + y = -5.618051264 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + y = -5.618051264 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + y = -5.618051264 + 4.75 y = -5.618051264 + 4.75 Combine like terms: -5.618051264 + 4.75 = -0.868051264 y = -0.868051264 Simplifying y = -0.868051264Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.368051264, -0.868051264}
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