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Simplifying 42 + -1y2 + -4y = 9 Reorder the terms: 42 + -4y + -1y2 = 9 Solving 42 + -4y + -1y2 = 9 Solving for variable 'y'. Reorder the terms: 42 + -9 + -4y + -1y2 = 9 + -9 Combine like terms: 42 + -9 = 33 33 + -4y + -1y2 = 9 + -9 Combine like terms: 9 + -9 = 0 33 + -4y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -33 + 4y + y2 = 0 Move the constant term to the right: Add '33' to each side of the equation. -33 + 4y + 33 + y2 = 0 + 33 Reorder the terms: -33 + 33 + 4y + y2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 4y + y2 = 0 + 33 4y + y2 = 0 + 33 Combine like terms: 0 + 33 = 33 4y + y2 = 33 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = 33 + 4 Reorder the terms: 4 + 4y + y2 = 33 + 4 Combine like terms: 33 + 4 = 37 4 + 4y + y2 = 37 Factor a perfect square on the left side: (y + 2)(y + 2) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (y + 2) equal to 6.08276253 and -6.08276253.Subproblem 1
y + 2 = 6.08276253 Simplifying y + 2 = 6.08276253 Reorder the terms: 2 + y = 6.08276253 Solving 2 + y = 6.08276253 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 6.08276253 + -2 Combine like terms: 2 + -2 = 0 0 + y = 6.08276253 + -2 y = 6.08276253 + -2 Combine like terms: 6.08276253 + -2 = 4.08276253 y = 4.08276253 Simplifying y = 4.08276253Subproblem 2
y + 2 = -6.08276253 Simplifying y + 2 = -6.08276253 Reorder the terms: 2 + y = -6.08276253 Solving 2 + y = -6.08276253 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -6.08276253 + -2 Combine like terms: 2 + -2 = 0 0 + y = -6.08276253 + -2 y = -6.08276253 + -2 Combine like terms: -6.08276253 + -2 = -8.08276253 y = -8.08276253 Simplifying y = -8.08276253Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.08276253, -8.08276253}
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