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Simplifying (6y2 + 3) + (4y2 + -7y + -5) = 0 Reorder the terms: (3 + 6y2) + (4y2 + -7y + -5) = 0 Remove parenthesis around (3 + 6y2) 3 + 6y2 + (4y2 + -7y + -5) = 0 Reorder the terms: 3 + 6y2 + (-5 + -7y + 4y2) = 0 Remove parenthesis around (-5 + -7y + 4y2) 3 + 6y2 + -5 + -7y + 4y2 = 0 Reorder the terms: 3 + -5 + -7y + 6y2 + 4y2 = 0 Combine like terms: 3 + -5 = -2 -2 + -7y + 6y2 + 4y2 = 0 Combine like terms: 6y2 + 4y2 = 10y2 -2 + -7y + 10y2 = 0 Solving -2 + -7y + 10y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.2 + -0.7y + y2 = 0.0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.7y + 0.2 + y2 = 0.0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.7y + y2 = 0.0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.7y + y2 = 0.0 + 0.2 -0.7y + y2 = 0.0 + 0.2 Combine like terms: 0.0 + 0.2 = 0.2 -0.7y + y2 = 0.2 The y term is -0.7y. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7y + 0.1225 + y2 = 0.2 + 0.1225 Reorder the terms: 0.1225 + -0.7y + y2 = 0.2 + 0.1225 Combine like terms: 0.2 + 0.1225 = 0.3225 0.1225 + -0.7y + y2 = 0.3225 Factor a perfect square on the left side: (y + -0.35)(y + -0.35) = 0.3225 Calculate the square root of the right side: 0.567890835 Break this problem into two subproblems by setting (y + -0.35) equal to 0.567890835 and -0.567890835.Subproblem 1
y + -0.35 = 0.567890835 Simplifying y + -0.35 = 0.567890835 Reorder the terms: -0.35 + y = 0.567890835 Solving -0.35 + y = 0.567890835 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + y = 0.567890835 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + y = 0.567890835 + 0.35 y = 0.567890835 + 0.35 Combine like terms: 0.567890835 + 0.35 = 0.917890835 y = 0.917890835 Simplifying y = 0.917890835Subproblem 2
y + -0.35 = -0.567890835 Simplifying y + -0.35 = -0.567890835 Reorder the terms: -0.35 + y = -0.567890835 Solving -0.35 + y = -0.567890835 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + y = -0.567890835 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + y = -0.567890835 + 0.35 y = -0.567890835 + 0.35 Combine like terms: -0.567890835 + 0.35 = -0.217890835 y = -0.217890835 Simplifying y = -0.217890835Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.917890835, -0.217890835}
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