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Simplifying 150 = 2y2 + -7y + 140 Reorder the terms: 150 = 140 + -7y + 2y2 Solving 150 = 140 + -7y + 2y2 Solving for variable 'y'. Combine like terms: 150 + -140 = 10 10 + 7y + -2y2 = 140 + -7y + 2y2 + -140 + 7y + -2y2 Reorder the terms: 10 + 7y + -2y2 = 140 + -140 + -7y + 7y + 2y2 + -2y2 Combine like terms: 140 + -140 = 0 10 + 7y + -2y2 = 0 + -7y + 7y + 2y2 + -2y2 10 + 7y + -2y2 = -7y + 7y + 2y2 + -2y2 Combine like terms: -7y + 7y = 0 10 + 7y + -2y2 = 0 + 2y2 + -2y2 10 + 7y + -2y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 10 + 7y + -2y2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -5 + -3.5y + y2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -3.5y + 5 + y2 = 0 + 5 Reorder the terms: -5 + 5 + -3.5y + y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3.5y + y2 = 0 + 5 -3.5y + y2 = 0 + 5 Combine like terms: 0 + 5 = 5 -3.5y + y2 = 5 The y term is -3.5y. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5y + 3.0625 + y2 = 5 + 3.0625 Reorder the terms: 3.0625 + -3.5y + y2 = 5 + 3.0625 Combine like terms: 5 + 3.0625 = 8.0625 3.0625 + -3.5y + y2 = 8.0625 Factor a perfect square on the left side: (y + -1.75)(y + -1.75) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (y + -1.75) equal to 2.839454173 and -2.839454173.Subproblem 1
y + -1.75 = 2.839454173 Simplifying y + -1.75 = 2.839454173 Reorder the terms: -1.75 + y = 2.839454173 Solving -1.75 + y = 2.839454173 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = 2.839454173 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = 2.839454173 + 1.75 y = 2.839454173 + 1.75 Combine like terms: 2.839454173 + 1.75 = 4.589454173 y = 4.589454173 Simplifying y = 4.589454173Subproblem 2
y + -1.75 = -2.839454173 Simplifying y + -1.75 = -2.839454173 Reorder the terms: -1.75 + y = -2.839454173 Solving -1.75 + y = -2.839454173 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = -2.839454173 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = -2.839454173 + 1.75 y = -2.839454173 + 1.75 Combine like terms: -2.839454173 + 1.75 = -1.089454173 y = -1.089454173 Simplifying y = -1.089454173Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.589454173, -1.089454173}
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