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Simplifying 7y2 + -8y + 15 + -11y2 + -8y + 6 = 0 Reorder the terms: 15 + 6 + -8y + -8y + 7y2 + -11y2 = 0 Combine like terms: 15 + 6 = 21 21 + -8y + -8y + 7y2 + -11y2 = 0 Combine like terms: -8y + -8y = -16y 21 + -16y + 7y2 + -11y2 = 0 Combine like terms: 7y2 + -11y2 = -4y2 21 + -16y + -4y2 = 0 Solving 21 + -16y + -4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -5.25 + 4y + y2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 4y + 5.25 + y2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 4y + y2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 4y + y2 = 0 + 5.25 4y + y2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 4y + y2 = 5.25 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 = 5.25 + 4 Reorder the terms: 4 + 4y + y2 = 5.25 + 4 Combine like terms: 5.25 + 4 = 9.25 4 + 4y + y2 = 9.25 Factor a perfect square on the left side: (y + 2)(y + 2) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (y + 2) equal to 3.041381265 and -3.041381265.Subproblem 1
y + 2 = 3.041381265 Simplifying y + 2 = 3.041381265 Reorder the terms: 2 + y = 3.041381265 Solving 2 + y = 3.041381265 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 = 3.041381265 + -2 Combine like terms: 2 + -2 = 0 0 + y = 3.041381265 + -2 y = 3.041381265 + -2 Combine like terms: 3.041381265 + -2 = 1.041381265 y = 1.041381265 Simplifying y = 1.041381265Subproblem 2
y + 2 = -3.041381265 Simplifying y + 2 = -3.041381265 Reorder the terms: 2 + y = -3.041381265 Solving 2 + y = -3.041381265 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 = -3.041381265 + -2 Combine like terms: 2 + -2 = 0 0 + y = -3.041381265 + -2 y = -3.041381265 + -2 Combine like terms: -3.041381265 + -2 = -5.041381265 y = -5.041381265 Simplifying y = -5.041381265Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.041381265, -5.041381265}
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