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Simplifying 4y(2y + -3) + -5(2 + -1y) = 0 Reorder the terms: 4y(-3 + 2y) + -5(2 + -1y) = 0 (-3 * 4y + 2y * 4y) + -5(2 + -1y) = 0 (-12y + 8y2) + -5(2 + -1y) = 0 -12y + 8y2 + (2 * -5 + -1y * -5) = 0 -12y + 8y2 + (-10 + 5y) = 0 Reorder the terms: -10 + -12y + 5y + 8y2 = 0 Combine like terms: -12y + 5y = -7y -10 + -7y + 8y2 = 0 Solving -10 + -7y + 8y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.25 + -0.875y + y2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -0.875y + 1.25 + y2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -0.875y + y2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -0.875y + y2 = 0 + 1.25 -0.875y + y2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -0.875y + y2 = 1.25 The y term is -0.875y. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875y + 0.19140625 + y2 = 1.25 + 0.19140625 Reorder the terms: 0.19140625 + -0.875y + y2 = 1.25 + 0.19140625 Combine like terms: 1.25 + 0.19140625 = 1.44140625 0.19140625 + -0.875y + y2 = 1.44140625 Factor a perfect square on the left side: (y + -0.4375)(y + -0.4375) = 1.44140625 Calculate the square root of the right side: 1.200585795 Break this problem into two subproblems by setting (y + -0.4375) equal to 1.200585795 and -1.200585795.Subproblem 1
y + -0.4375 = 1.200585795 Simplifying y + -0.4375 = 1.200585795 Reorder the terms: -0.4375 + y = 1.200585795 Solving -0.4375 + y = 1.200585795 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + y = 1.200585795 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + y = 1.200585795 + 0.4375 y = 1.200585795 + 0.4375 Combine like terms: 1.200585795 + 0.4375 = 1.638085795 y = 1.638085795 Simplifying y = 1.638085795Subproblem 2
y + -0.4375 = -1.200585795 Simplifying y + -0.4375 = -1.200585795 Reorder the terms: -0.4375 + y = -1.200585795 Solving -0.4375 + y = -1.200585795 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + y = -1.200585795 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + y = -1.200585795 + 0.4375 y = -1.200585795 + 0.4375 Combine like terms: -1.200585795 + 0.4375 = -0.763085795 y = -0.763085795 Simplifying y = -0.763085795Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.638085795, -0.763085795}
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