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Simplifying 5y2 + 10y + -48 = 0 Reorder the terms: -48 + 10y + 5y2 = 0 Solving -48 + 10y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.6 + 2y + y2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + 2y + 9.6 + y2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + 2y + y2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + 2y + y2 = 0 + 9.6 2y + y2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 2y + y2 = 9.6 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 9.6 + 1 Reorder the terms: 1 + 2y + y2 = 9.6 + 1 Combine like terms: 9.6 + 1 = 10.6 1 + 2y + y2 = 10.6 Factor a perfect square on the left side: (y + 1)(y + 1) = 10.6 Calculate the square root of the right side: 3.255764119 Break this problem into two subproblems by setting (y + 1) equal to 3.255764119 and -3.255764119.Subproblem 1
y + 1 = 3.255764119 Simplifying y + 1 = 3.255764119 Reorder the terms: 1 + y = 3.255764119 Solving 1 + y = 3.255764119 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 3.255764119 + -1 Combine like terms: 1 + -1 = 0 0 + y = 3.255764119 + -1 y = 3.255764119 + -1 Combine like terms: 3.255764119 + -1 = 2.255764119 y = 2.255764119 Simplifying y = 2.255764119Subproblem 2
y + 1 = -3.255764119 Simplifying y + 1 = -3.255764119 Reorder the terms: 1 + y = -3.255764119 Solving 1 + y = -3.255764119 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -3.255764119 + -1 Combine like terms: 1 + -1 = 0 0 + y = -3.255764119 + -1 y = -3.255764119 + -1 Combine like terms: -3.255764119 + -1 = -4.255764119 y = -4.255764119 Simplifying y = -4.255764119Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.255764119, -4.255764119}
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