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Simplifying 100 + -4y2 + -3y = 0 Reorder the terms: 100 + -3y + -4y2 = 0 Solving 100 + -3y + -4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -25 + 0.75y + y2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 0.75y + 25 + y2 = 0 + 25 Reorder the terms: -25 + 25 + 0.75y + y2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 0.75y + y2 = 0 + 25 0.75y + y2 = 0 + 25 Combine like terms: 0 + 25 = 25 0.75y + y2 = 25 The y term is 0.75y. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75y + 0.140625 + y2 = 25 + 0.140625 Reorder the terms: 0.140625 + 0.75y + y2 = 25 + 0.140625 Combine like terms: 25 + 0.140625 = 25.140625 0.140625 + 0.75y + y2 = 25.140625 Factor a perfect square on the left side: (y + 0.375)(y + 0.375) = 25.140625 Calculate the square root of the right side: 5.01404278 Break this problem into two subproblems by setting (y + 0.375) equal to 5.01404278 and -5.01404278.Subproblem 1
y + 0.375 = 5.01404278 Simplifying y + 0.375 = 5.01404278 Reorder the terms: 0.375 + y = 5.01404278 Solving 0.375 + y = 5.01404278 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + y = 5.01404278 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + y = 5.01404278 + -0.375 y = 5.01404278 + -0.375 Combine like terms: 5.01404278 + -0.375 = 4.63904278 y = 4.63904278 Simplifying y = 4.63904278Subproblem 2
y + 0.375 = -5.01404278 Simplifying y + 0.375 = -5.01404278 Reorder the terms: 0.375 + y = -5.01404278 Solving 0.375 + y = -5.01404278 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + y = -5.01404278 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + y = -5.01404278 + -0.375 y = -5.01404278 + -0.375 Combine like terms: -5.01404278 + -0.375 = -5.38904278 y = -5.38904278 Simplifying y = -5.38904278Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.63904278, -5.38904278}
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