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Simplifying 2y2 + 10y + -5 = 3y2 + -30 Reorder the terms: -5 + 10y + 2y2 = 3y2 + -30 Reorder the terms: -5 + 10y + 2y2 = -30 + 3y2 Solving -5 + 10y + 2y2 = -30 + 3y2 Solving for variable 'y'. Reorder the terms: -5 + 30 + 10y + 2y2 + -3y2 = -30 + 3y2 + 30 + -3y2 Combine like terms: -5 + 30 = 25 25 + 10y + 2y2 + -3y2 = -30 + 3y2 + 30 + -3y2 Combine like terms: 2y2 + -3y2 = -1y2 25 + 10y + -1y2 = -30 + 3y2 + 30 + -3y2 Reorder the terms: 25 + 10y + -1y2 = -30 + 30 + 3y2 + -3y2 Combine like terms: -30 + 30 = 0 25 + 10y + -1y2 = 0 + 3y2 + -3y2 25 + 10y + -1y2 = 3y2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 25 + 10y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + -10y + y2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -10y + 25 + y2 = 0 + 25 Reorder the terms: -25 + 25 + -10y + y2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -10y + y2 = 0 + 25 -10y + y2 = 0 + 25 Combine like terms: 0 + 25 = 25 -10y + y2 = 25 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = 25 + 25 Reorder the terms: 25 + -10y + y2 = 25 + 25 Combine like terms: 25 + 25 = 50 25 + -10y + y2 = 50 Factor a perfect square on the left side: (y + -5)(y + -5) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (y + -5) equal to 7.071067812 and -7.071067812.Subproblem 1
y + -5 = 7.071067812 Simplifying y + -5 = 7.071067812 Reorder the terms: -5 + y = 7.071067812 Solving -5 + y = 7.071067812 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 7.071067812 + 5 Combine like terms: -5 + 5 = 0 0 + y = 7.071067812 + 5 y = 7.071067812 + 5 Combine like terms: 7.071067812 + 5 = 12.071067812 y = 12.071067812 Simplifying y = 12.071067812Subproblem 2
y + -5 = -7.071067812 Simplifying y + -5 = -7.071067812 Reorder the terms: -5 + y = -7.071067812 Solving -5 + y = -7.071067812 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -7.071067812 + 5 Combine like terms: -5 + 5 = 0 0 + y = -7.071067812 + 5 y = -7.071067812 + 5 Combine like terms: -7.071067812 + 5 = -2.071067812 y = -2.071067812 Simplifying y = -2.071067812Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.071067812, -2.071067812}
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