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Simplifying 5y2 = 3y + 4 Reorder the terms: 5y2 = 4 + 3y Solving 5y2 = 4 + 3y Solving for variable 'y'. Reorder the terms: -4 + -3y + 5y2 = 4 + 3y + -4 + -3y Reorder the terms: -4 + -3y + 5y2 = 4 + -4 + 3y + -3y Combine like terms: 4 + -4 = 0 -4 + -3y + 5y2 = 0 + 3y + -3y -4 + -3y + 5y2 = 3y + -3y Combine like terms: 3y + -3y = 0 -4 + -3y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -0.6y + y2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -0.6y + 0.8 + y2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -0.6y + y2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -0.6y + y2 = 0 + 0.8 -0.6y + y2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -0.6y + y2 = 0.8 The y term is -0.6y. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6y + 0.09 + y2 = 0.8 + 0.09 Reorder the terms: 0.09 + -0.6y + y2 = 0.8 + 0.09 Combine like terms: 0.8 + 0.09 = 0.89 0.09 + -0.6y + y2 = 0.89 Factor a perfect square on the left side: (y + -0.3)(y + -0.3) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (y + -0.3) equal to 0.943398113 and -0.943398113.Subproblem 1
y + -0.3 = 0.943398113 Simplifying y + -0.3 = 0.943398113 Reorder the terms: -0.3 + y = 0.943398113 Solving -0.3 + y = 0.943398113 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + y = 0.943398113 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + y = 0.943398113 + 0.3 y = 0.943398113 + 0.3 Combine like terms: 0.943398113 + 0.3 = 1.243398113 y = 1.243398113 Simplifying y = 1.243398113Subproblem 2
y + -0.3 = -0.943398113 Simplifying y + -0.3 = -0.943398113 Reorder the terms: -0.3 + y = -0.943398113 Solving -0.3 + y = -0.943398113 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + y = -0.943398113 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + y = -0.943398113 + 0.3 y = -0.943398113 + 0.3 Combine like terms: -0.943398113 + 0.3 = -0.643398113 y = -0.643398113 Simplifying y = -0.643398113Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.243398113, -0.643398113}
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