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Simplifying -5y(3y + -5) + 4(2y + 10) = 0 Reorder the terms: -5y(-5 + 3y) + 4(2y + 10) = 0 (-5 * -5y + 3y * -5y) + 4(2y + 10) = 0 (25y + -15y2) + 4(2y + 10) = 0 Reorder the terms: 25y + -15y2 + 4(10 + 2y) = 0 25y + -15y2 + (10 * 4 + 2y * 4) = 0 25y + -15y2 + (40 + 8y) = 0 Reorder the terms: 40 + 25y + 8y + -15y2 = 0 Combine like terms: 25y + 8y = 33y 40 + 33y + -15y2 = 0 Solving 40 + 33y + -15y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -2.666666667 + -2.2y + y2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -2.2y + 2.666666667 + y2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -2.2y + y2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -2.2y + y2 = 0 + 2.666666667 -2.2y + y2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -2.2y + y2 = 2.666666667 The y term is -2.2y. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2y + 1.21 + y2 = 2.666666667 + 1.21 Reorder the terms: 1.21 + -2.2y + y2 = 2.666666667 + 1.21 Combine like terms: 2.666666667 + 1.21 = 3.876666667 1.21 + -2.2y + y2 = 3.876666667 Factor a perfect square on the left side: (y + -1.1)(y + -1.1) = 3.876666667 Calculate the square root of the right side: 1.968925257 Break this problem into two subproblems by setting (y + -1.1) equal to 1.968925257 and -1.968925257.Subproblem 1
y + -1.1 = 1.968925257 Simplifying y + -1.1 = 1.968925257 Reorder the terms: -1.1 + y = 1.968925257 Solving -1.1 + y = 1.968925257 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + y = 1.968925257 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + y = 1.968925257 + 1.1 y = 1.968925257 + 1.1 Combine like terms: 1.968925257 + 1.1 = 3.068925257 y = 3.068925257 Simplifying y = 3.068925257Subproblem 2
y + -1.1 = -1.968925257 Simplifying y + -1.1 = -1.968925257 Reorder the terms: -1.1 + y = -1.968925257 Solving -1.1 + y = -1.968925257 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + y = -1.968925257 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + y = -1.968925257 + 1.1 y = -1.968925257 + 1.1 Combine like terms: -1.968925257 + 1.1 = -0.868925257 y = -0.868925257 Simplifying y = -0.868925257Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.068925257, -0.868925257}
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