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Simplifying 10y2 = 16y + 5 Reorder the terms: 10y2 = 5 + 16y Solving 10y2 = 5 + 16y Solving for variable 'y'. Reorder the terms: -5 + -16y + 10y2 = 5 + 16y + -5 + -16y Reorder the terms: -5 + -16y + 10y2 = 5 + -5 + 16y + -16y Combine like terms: 5 + -5 = 0 -5 + -16y + 10y2 = 0 + 16y + -16y -5 + -16y + 10y2 = 16y + -16y Combine like terms: 16y + -16y = 0 -5 + -16y + 10y2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.5 + -1.6y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.6y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.6y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.6y + y2 = 0 + 0.5 -1.6y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1.6y + y2 = 0.5 The y term is -1.6y. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6y + 0.64 + y2 = 0.5 + 0.64 Reorder the terms: 0.64 + -1.6y + y2 = 0.5 + 0.64 Combine like terms: 0.5 + 0.64 = 1.14 0.64 + -1.6y + y2 = 1.14 Factor a perfect square on the left side: (y + -0.8)(y + -0.8) = 1.14 Calculate the square root of the right side: 1.067707825 Break this problem into two subproblems by setting (y + -0.8) equal to 1.067707825 and -1.067707825.Subproblem 1
y + -0.8 = 1.067707825 Simplifying y + -0.8 = 1.067707825 Reorder the terms: -0.8 + y = 1.067707825 Solving -0.8 + y = 1.067707825 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + y = 1.067707825 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + y = 1.067707825 + 0.8 y = 1.067707825 + 0.8 Combine like terms: 1.067707825 + 0.8 = 1.867707825 y = 1.867707825 Simplifying y = 1.867707825Subproblem 2
y + -0.8 = -1.067707825 Simplifying y + -0.8 = -1.067707825 Reorder the terms: -0.8 + y = -1.067707825 Solving -0.8 + y = -1.067707825 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + y = -1.067707825 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + y = -1.067707825 + 0.8 y = -1.067707825 + 0.8 Combine like terms: -1.067707825 + 0.8 = -0.267707825 y = -0.267707825 Simplifying y = -0.267707825Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.867707825, -0.267707825}
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