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Simplifying (7y2 + 6y + -9) + -1(2y2 + -8y + 8) = 0 Reorder the terms: (-9 + 6y + 7y2) + -1(2y2 + -8y + 8) = 0 Remove parenthesis around (-9 + 6y + 7y2) -9 + 6y + 7y2 + -1(2y2 + -8y + 8) = 0 Reorder the terms: -9 + 6y + 7y2 + -1(8 + -8y + 2y2) = 0 -9 + 6y + 7y2 + (8 * -1 + -8y * -1 + 2y2 * -1) = 0 -9 + 6y + 7y2 + (-8 + 8y + -2y2) = 0 Reorder the terms: -9 + -8 + 6y + 8y + 7y2 + -2y2 = 0 Combine like terms: -9 + -8 = -17 -17 + 6y + 8y + 7y2 + -2y2 = 0 Combine like terms: 6y + 8y = 14y -17 + 14y + 7y2 + -2y2 = 0 Combine like terms: 7y2 + -2y2 = 5y2 -17 + 14y + 5y2 = 0 Solving -17 + 14y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.4 + 2.8y + y2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + 2.8y + 3.4 + y2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + 2.8y + y2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + 2.8y + y2 = 0 + 3.4 2.8y + y2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 2.8y + y2 = 3.4 The y term is 2.8y. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8y + 1.96 + y2 = 3.4 + 1.96 Reorder the terms: 1.96 + 2.8y + y2 = 3.4 + 1.96 Combine like terms: 3.4 + 1.96 = 5.36 1.96 + 2.8y + y2 = 5.36 Factor a perfect square on the left side: (y + 1.4)(y + 1.4) = 5.36 Calculate the square root of the right side: 2.315167381 Break this problem into two subproblems by setting (y + 1.4) equal to 2.315167381 and -2.315167381.Subproblem 1
y + 1.4 = 2.315167381 Simplifying y + 1.4 = 2.315167381 Reorder the terms: 1.4 + y = 2.315167381 Solving 1.4 + y = 2.315167381 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + y = 2.315167381 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + y = 2.315167381 + -1.4 y = 2.315167381 + -1.4 Combine like terms: 2.315167381 + -1.4 = 0.915167381 y = 0.915167381 Simplifying y = 0.915167381Subproblem 2
y + 1.4 = -2.315167381 Simplifying y + 1.4 = -2.315167381 Reorder the terms: 1.4 + y = -2.315167381 Solving 1.4 + y = -2.315167381 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + y = -2.315167381 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + y = -2.315167381 + -1.4 y = -2.315167381 + -1.4 Combine like terms: -2.315167381 + -1.4 = -3.715167381 y = -3.715167381 Simplifying y = -3.715167381Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.915167381, -3.715167381}
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