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Simplifying 5y2 + -19y + 6 = 0 Reorder the terms: 6 + -19y + 5y2 = 0 Solving 6 + -19y + 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'. 1.2 + -3.8y + y2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -3.8y + -1.2 + y2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -3.8y + y2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -3.8y + y2 = 0 + -1.2 -3.8y + y2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -3.8y + y2 = -1.2 The y term is -3.8y. Take half its coefficient (-1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. -3.8y + 3.61 + y2 = -1.2 + 3.61 Reorder the terms: 3.61 + -3.8y + y2 = -1.2 + 3.61 Combine like terms: -1.2 + 3.61 = 2.41 3.61 + -3.8y + y2 = 2.41 Factor a perfect square on the left side: (y + -1.9)(y + -1.9) = 2.41 Calculate the square root of the right side: 1.55241747 Break this problem into two subproblems by setting (y + -1.9) equal to 1.55241747 and -1.55241747.Subproblem 1
y + -1.9 = 1.55241747 Simplifying y + -1.9 = 1.55241747 Reorder the terms: -1.9 + y = 1.55241747 Solving -1.9 + y = 1.55241747 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + y = 1.55241747 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + y = 1.55241747 + 1.9 y = 1.55241747 + 1.9 Combine like terms: 1.55241747 + 1.9 = 3.45241747 y = 3.45241747 Simplifying y = 3.45241747Subproblem 2
y + -1.9 = -1.55241747 Simplifying y + -1.9 = -1.55241747 Reorder the terms: -1.9 + y = -1.55241747 Solving -1.9 + y = -1.55241747 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + y = -1.55241747 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + y = -1.55241747 + 1.9 y = -1.55241747 + 1.9 Combine like terms: -1.55241747 + 1.9 = 0.34758253 y = 0.34758253 Simplifying y = 0.34758253Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.45241747, 0.34758253}
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