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Simplifying 19y2 + -18y + -16 = 0 Reorder the terms: -16 + -18y + 19y2 = 0 Solving -16 + -18y + 19y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -0.8421052632 + -0.9473684211y + y2 = 0 Move the constant term to the right: Add '0.8421052632' to each side of the equation. -0.8421052632 + -0.9473684211y + 0.8421052632 + y2 = 0 + 0.8421052632 Reorder the terms: -0.8421052632 + 0.8421052632 + -0.9473684211y + y2 = 0 + 0.8421052632 Combine like terms: -0.8421052632 + 0.8421052632 = 0.0000000000 0.0000000000 + -0.9473684211y + y2 = 0 + 0.8421052632 -0.9473684211y + y2 = 0 + 0.8421052632 Combine like terms: 0 + 0.8421052632 = 0.8421052632 -0.9473684211y + y2 = 0.8421052632 The y term is -0.9473684211y. Take half its coefficient (-0.4736842106). Square it (0.2243767314) and add it to both sides. Add '0.2243767314' to each side of the equation. -0.9473684211y + 0.2243767314 + y2 = 0.8421052632 + 0.2243767314 Reorder the terms: 0.2243767314 + -0.9473684211y + y2 = 0.8421052632 + 0.2243767314 Combine like terms: 0.8421052632 + 0.2243767314 = 1.0664819946 0.2243767314 + -0.9473684211y + y2 = 1.0664819946 Factor a perfect square on the left side: (y + -0.4736842106)(y + -0.4736842106) = 1.0664819946 Calculate the square root of the right side: 1.032706151 Break this problem into two subproblems by setting (y + -0.4736842106) equal to 1.032706151 and -1.032706151.Subproblem 1
y + -0.4736842106 = 1.032706151 Simplifying y + -0.4736842106 = 1.032706151 Reorder the terms: -0.4736842106 + y = 1.032706151 Solving -0.4736842106 + y = 1.032706151 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4736842106' to each side of the equation. -0.4736842106 + 0.4736842106 + y = 1.032706151 + 0.4736842106 Combine like terms: -0.4736842106 + 0.4736842106 = 0.0000000000 0.0000000000 + y = 1.032706151 + 0.4736842106 y = 1.032706151 + 0.4736842106 Combine like terms: 1.032706151 + 0.4736842106 = 1.5063903616 y = 1.5063903616 Simplifying y = 1.5063903616Subproblem 2
y + -0.4736842106 = -1.032706151 Simplifying y + -0.4736842106 = -1.032706151 Reorder the terms: -0.4736842106 + y = -1.032706151 Solving -0.4736842106 + y = -1.032706151 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4736842106' to each side of the equation. -0.4736842106 + 0.4736842106 + y = -1.032706151 + 0.4736842106 Combine like terms: -0.4736842106 + 0.4736842106 = 0.0000000000 0.0000000000 + y = -1.032706151 + 0.4736842106 y = -1.032706151 + 0.4736842106 Combine like terms: -1.032706151 + 0.4736842106 = -0.5590219404 y = -0.5590219404 Simplifying y = -0.5590219404Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.5063903616, -0.5590219404}
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