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Simplifying -1(-3.0625 + -0.125y + 0.1875y2) + y = 4 (-3.0625 * -1 + -0.125y * -1 + 0.1875y2 * -1) + y = 4 (3.0625 + 0.125y + -0.1875y2) + y = 4 Reorder the terms: 3.0625 + 0.125y + y + -0.1875y2 = 4 Combine like terms: 0.125y + y = 1.125y 3.0625 + 1.125y + -0.1875y2 = 4 Solving 3.0625 + 1.125y + -0.1875y2 = 4 Solving for variable 'y'. Reorder the terms: 3.0625 + -4 + 1.125y + -0.1875y2 = 4 + -4 Combine like terms: 3.0625 + -4 = -0.9375 -0.9375 + 1.125y + -0.1875y2 = 4 + -4 Combine like terms: 4 + -4 = 0 -0.9375 + 1.125y + -0.1875y2 = 0 Begin completing the square. Divide all terms by -0.1875 the coefficient of the squared term: Divide each side by '-0.1875'. 5 + -6y + y2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -6y + -5 + y2 = 0 + -5 Reorder the terms: 5 + -5 + -6y + y2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6y + y2 = 0 + -5 -6y + y2 = 0 + -5 Combine like terms: 0 + -5 = -5 -6y + y2 = -5 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = -5 + 9 Reorder the terms: 9 + -6y + y2 = -5 + 9 Combine like terms: -5 + 9 = 4 9 + -6y + y2 = 4 Factor a perfect square on the left side: (y + -3)(y + -3) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (y + -3) equal to 2 and -2.Subproblem 1
y + -3 = 2 Simplifying y + -3 = 2 Reorder the terms: -3 + y = 2 Solving -3 + y = 2 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 2 + 3 Combine like terms: -3 + 3 = 0 0 + y = 2 + 3 y = 2 + 3 Combine like terms: 2 + 3 = 5 y = 5 Simplifying y = 5Subproblem 2
y + -3 = -2 Simplifying y + -3 = -2 Reorder the terms: -3 + y = -2 Solving -3 + y = -2 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -2 + 3 Combine like terms: -3 + 3 = 0 0 + y = -2 + 3 y = -2 + 3 Combine like terms: -2 + 3 = 1 y = 1 Simplifying y = 1Solution
The solution to the problem is based on the solutions from the subproblems. y = {5, 1}
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