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Simplifying (-6y2 + 5y + -2) + (y2 + 3y + 7) = 0 Reorder the terms: (-2 + 5y + -6y2) + (y2 + 3y + 7) = 0 Remove parenthesis around (-2 + 5y + -6y2) -2 + 5y + -6y2 + (y2 + 3y + 7) = 0 Reorder the terms: -2 + 5y + -6y2 + (7 + 3y + y2) = 0 Remove parenthesis around (7 + 3y + y2) -2 + 5y + -6y2 + 7 + 3y + y2 = 0 Reorder the terms: -2 + 7 + 5y + 3y + -6y2 + y2 = 0 Combine like terms: -2 + 7 = 5 5 + 5y + 3y + -6y2 + y2 = 0 Combine like terms: 5y + 3y = 8y 5 + 8y + -6y2 + y2 = 0 Combine like terms: -6y2 + y2 = -5y2 5 + 8y + -5y2 = 0 Solving 5 + 8y + -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 + -1.6y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.6y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -1.6y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.6y + y2 = 0 + 1 -1.6y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.6y + y2 = 1 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 = 1 + 0.64 Reorder the terms: 0.64 + -1.6y + y2 = 1 + 0.64 Combine like terms: 1 + 0.64 = 1.64 0.64 + -1.6y + y2 = 1.64 Factor a perfect square on the left side: (y + -0.8)(y + -0.8) = 1.64 Calculate the square root of the right side: 1.280624847 Break this problem into two subproblems by setting (y + -0.8) equal to 1.280624847 and -1.280624847.Subproblem 1
y + -0.8 = 1.280624847 Simplifying y + -0.8 = 1.280624847 Reorder the terms: -0.8 + y = 1.280624847 Solving -0.8 + y = 1.280624847 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 = 1.280624847 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + y = 1.280624847 + 0.8 y = 1.280624847 + 0.8 Combine like terms: 1.280624847 + 0.8 = 2.080624847 y = 2.080624847 Simplifying y = 2.080624847Subproblem 2
y + -0.8 = -1.280624847 Simplifying y + -0.8 = -1.280624847 Reorder the terms: -0.8 + y = -1.280624847 Solving -0.8 + y = -1.280624847 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 = -1.280624847 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + y = -1.280624847 + 0.8 y = -1.280624847 + 0.8 Combine like terms: -1.280624847 + 0.8 = -0.480624847 y = -0.480624847 Simplifying y = -0.480624847Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.080624847, -0.480624847}
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