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Simplifying 4y(11y + -14) = 6 + -3y Reorder the terms: 4y(-14 + 11y) = 6 + -3y (-14 * 4y + 11y * 4y) = 6 + -3y (-56y + 44y2) = 6 + -3y Solving -56y + 44y2 = 6 + -3y Solving for variable 'y'. Reorder the terms: -6 + -56y + 3y + 44y2 = 6 + -3y + -6 + 3y Combine like terms: -56y + 3y = -53y -6 + -53y + 44y2 = 6 + -3y + -6 + 3y Reorder the terms: -6 + -53y + 44y2 = 6 + -6 + -3y + 3y Combine like terms: 6 + -6 = 0 -6 + -53y + 44y2 = 0 + -3y + 3y -6 + -53y + 44y2 = -3y + 3y Combine like terms: -3y + 3y = 0 -6 + -53y + 44y2 = 0 Begin completing the square. Divide all terms by 44 the coefficient of the squared term: Divide each side by '44'. -0.1363636364 + -1.204545455y + y2 = 0 Move the constant term to the right: Add '0.1363636364' to each side of the equation. -0.1363636364 + -1.204545455y + 0.1363636364 + y2 = 0 + 0.1363636364 Reorder the terms: -0.1363636364 + 0.1363636364 + -1.204545455y + y2 = 0 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + -1.204545455y + y2 = 0 + 0.1363636364 -1.204545455y + y2 = 0 + 0.1363636364 Combine like terms: 0 + 0.1363636364 = 0.1363636364 -1.204545455y + y2 = 0.1363636364 The y term is -1.204545455y. Take half its coefficient (-0.6022727275). Square it (0.3627324383) and add it to both sides. Add '0.3627324383' to each side of the equation. -1.204545455y + 0.3627324383 + y2 = 0.1363636364 + 0.3627324383 Reorder the terms: 0.3627324383 + -1.204545455y + y2 = 0.1363636364 + 0.3627324383 Combine like terms: 0.1363636364 + 0.3627324383 = 0.4990960747 0.3627324383 + -1.204545455y + y2 = 0.4990960747 Factor a perfect square on the left side: (y + -0.6022727275)(y + -0.6022727275) = 0.4990960747 Calculate the square root of the right side: 0.70646732 Break this problem into two subproblems by setting (y + -0.6022727275) equal to 0.70646732 and -0.70646732.Subproblem 1
y + -0.6022727275 = 0.70646732 Simplifying y + -0.6022727275 = 0.70646732 Reorder the terms: -0.6022727275 + y = 0.70646732 Solving -0.6022727275 + y = 0.70646732 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6022727275' to each side of the equation. -0.6022727275 + 0.6022727275 + y = 0.70646732 + 0.6022727275 Combine like terms: -0.6022727275 + 0.6022727275 = 0.0000000000 0.0000000000 + y = 0.70646732 + 0.6022727275 y = 0.70646732 + 0.6022727275 Combine like terms: 0.70646732 + 0.6022727275 = 1.3087400475 y = 1.3087400475 Simplifying y = 1.3087400475Subproblem 2
y + -0.6022727275 = -0.70646732 Simplifying y + -0.6022727275 = -0.70646732 Reorder the terms: -0.6022727275 + y = -0.70646732 Solving -0.6022727275 + y = -0.70646732 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6022727275' to each side of the equation. -0.6022727275 + 0.6022727275 + y = -0.70646732 + 0.6022727275 Combine like terms: -0.6022727275 + 0.6022727275 = 0.0000000000 0.0000000000 + y = -0.70646732 + 0.6022727275 y = -0.70646732 + 0.6022727275 Combine like terms: -0.70646732 + 0.6022727275 = -0.1041945925 y = -0.1041945925 Simplifying y = -0.1041945925Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.3087400475, -0.1041945925}
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