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Simplifying (8y2 + 4y + -9) + -1(6y + 4) = 0 Reorder the terms: (-9 + 4y + 8y2) + -1(6y + 4) = 0 Remove parenthesis around (-9 + 4y + 8y2) -9 + 4y + 8y2 + -1(6y + 4) = 0 Reorder the terms: -9 + 4y + 8y2 + -1(4 + 6y) = 0 -9 + 4y + 8y2 + (4 * -1 + 6y * -1) = 0 -9 + 4y + 8y2 + (-4 + -6y) = 0 Reorder the terms: -9 + -4 + 4y + -6y + 8y2 = 0 Combine like terms: -9 + -4 = -13 -13 + 4y + -6y + 8y2 = 0 Combine like terms: 4y + -6y = -2y -13 + -2y + 8y2 = 0 Solving -13 + -2y + 8y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.625 + -0.25y + y2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + -0.25y + 1.625 + y2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + -0.25y + y2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + -0.25y + y2 = 0 + 1.625 -0.25y + y2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 -0.25y + y2 = 1.625 The y term is -0.25y. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25y + 0.015625 + y2 = 1.625 + 0.015625 Reorder the terms: 0.015625 + -0.25y + y2 = 1.625 + 0.015625 Combine like terms: 1.625 + 0.015625 = 1.640625 0.015625 + -0.25y + y2 = 1.640625 Factor a perfect square on the left side: (y + -0.125)(y + -0.125) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (y + -0.125) equal to 1.280868846 and -1.280868846.Subproblem 1
y + -0.125 = 1.280868846 Simplifying y + -0.125 = 1.280868846 Reorder the terms: -0.125 + y = 1.280868846 Solving -0.125 + y = 1.280868846 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + y = 1.280868846 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + y = 1.280868846 + 0.125 y = 1.280868846 + 0.125 Combine like terms: 1.280868846 + 0.125 = 1.405868846 y = 1.405868846 Simplifying y = 1.405868846Subproblem 2
y + -0.125 = -1.280868846 Simplifying y + -0.125 = -1.280868846 Reorder the terms: -0.125 + y = -1.280868846 Solving -0.125 + y = -1.280868846 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + y = -1.280868846 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + y = -1.280868846 + 0.125 y = -1.280868846 + 0.125 Combine like terms: -1.280868846 + 0.125 = -1.155868846 y = -1.155868846 Simplifying y = -1.155868846Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.405868846, -1.155868846}
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