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Simplifying 5y2 + -16y + -15 = 0 Reorder the terms: -15 + -16y + 5y2 = 0 Solving -15 + -16y + 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 + -3.2y + y2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -3.2y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + -3.2y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3.2y + y2 = 0 + 3 -3.2y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 -3.2y + y2 = 3 The y term is -3.2y. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2y + 2.56 + y2 = 3 + 2.56 Reorder the terms: 2.56 + -3.2y + y2 = 3 + 2.56 Combine like terms: 3 + 2.56 = 5.56 2.56 + -3.2y + y2 = 5.56 Factor a perfect square on the left side: (y + -1.6)(y + -1.6) = 5.56 Calculate the square root of the right side: 2.357965225 Break this problem into two subproblems by setting (y + -1.6) equal to 2.357965225 and -2.357965225.Subproblem 1
y + -1.6 = 2.357965225 Simplifying y + -1.6 = 2.357965225 Reorder the terms: -1.6 + y = 2.357965225 Solving -1.6 + y = 2.357965225 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + y = 2.357965225 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + y = 2.357965225 + 1.6 y = 2.357965225 + 1.6 Combine like terms: 2.357965225 + 1.6 = 3.957965225 y = 3.957965225 Simplifying y = 3.957965225Subproblem 2
y + -1.6 = -2.357965225 Simplifying y + -1.6 = -2.357965225 Reorder the terms: -1.6 + y = -2.357965225 Solving -1.6 + y = -2.357965225 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + y = -2.357965225 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + y = -2.357965225 + 1.6 y = -2.357965225 + 1.6 Combine like terms: -2.357965225 + 1.6 = -0.757965225 y = -0.757965225 Simplifying y = -0.757965225Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.957965225, -0.757965225}
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