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Simplifying 4y2 + -8y = 37 Reorder the terms: -8y + 4y2 = 37 Solving -8y + 4y2 = 37 Solving for variable 'y'. Reorder the terms: -37 + -8y + 4y2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + -8y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9.25 + -2y + y2 = 0 Move the constant term to the right: Add '9.25' to each side of the equation. -9.25 + -2y + 9.25 + y2 = 0 + 9.25 Reorder the terms: -9.25 + 9.25 + -2y + y2 = 0 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + -2y + y2 = 0 + 9.25 -2y + y2 = 0 + 9.25 Combine like terms: 0 + 9.25 = 9.25 -2y + y2 = 9.25 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 = 9.25 + 1 Reorder the terms: 1 + -2y + y2 = 9.25 + 1 Combine like terms: 9.25 + 1 = 10.25 1 + -2y + y2 = 10.25 Factor a perfect square on the left side: (y + -1)(y + -1) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (y + -1) equal to 3.201562119 and -3.201562119.Subproblem 1
y + -1 = 3.201562119 Simplifying y + -1 = 3.201562119 Reorder the terms: -1 + y = 3.201562119 Solving -1 + y = 3.201562119 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 = 3.201562119 + 1 Combine like terms: -1 + 1 = 0 0 + y = 3.201562119 + 1 y = 3.201562119 + 1 Combine like terms: 3.201562119 + 1 = 4.201562119 y = 4.201562119 Simplifying y = 4.201562119Subproblem 2
y + -1 = -3.201562119 Simplifying y + -1 = -3.201562119 Reorder the terms: -1 + y = -3.201562119 Solving -1 + y = -3.201562119 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 = -3.201562119 + 1 Combine like terms: -1 + 1 = 0 0 + y = -3.201562119 + 1 y = -3.201562119 + 1 Combine like terms: -3.201562119 + 1 = -2.201562119 y = -2.201562119 Simplifying y = -2.201562119Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.201562119, -2.201562119}
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