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Simplifying (y2 + -2y + 4) + (-6y2 + 5y + 7) = 0 Reorder the terms: (4 + -2y + y2) + (-6y2 + 5y + 7) = 0 Remove parenthesis around (4 + -2y + y2) 4 + -2y + y2 + (-6y2 + 5y + 7) = 0 Reorder the terms: 4 + -2y + y2 + (7 + 5y + -6y2) = 0 Remove parenthesis around (7 + 5y + -6y2) 4 + -2y + y2 + 7 + 5y + -6y2 = 0 Reorder the terms: 4 + 7 + -2y + 5y + y2 + -6y2 = 0 Combine like terms: 4 + 7 = 11 11 + -2y + 5y + y2 + -6y2 = 0 Combine like terms: -2y + 5y = 3y 11 + 3y + y2 + -6y2 = 0 Combine like terms: y2 + -6y2 = -5y2 11 + 3y + -5y2 = 0 Solving 11 + 3y + -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'. -2.2 + -0.6y + y2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -0.6y + 2.2 + y2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + -0.6y + y2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -0.6y + y2 = 0 + 2.2 -0.6y + y2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 -0.6y + y2 = 2.2 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 = 2.2 + 0.09 Reorder the terms: 0.09 + -0.6y + y2 = 2.2 + 0.09 Combine like terms: 2.2 + 0.09 = 2.29 0.09 + -0.6y + y2 = 2.29 Factor a perfect square on the left side: (y + -0.3)(y + -0.3) = 2.29 Calculate the square root of the right side: 1.513274595 Break this problem into two subproblems by setting (y + -0.3) equal to 1.513274595 and -1.513274595.Subproblem 1
y + -0.3 = 1.513274595 Simplifying y + -0.3 = 1.513274595 Reorder the terms: -0.3 + y = 1.513274595 Solving -0.3 + y = 1.513274595 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 = 1.513274595 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + y = 1.513274595 + 0.3 y = 1.513274595 + 0.3 Combine like terms: 1.513274595 + 0.3 = 1.813274595 y = 1.813274595 Simplifying y = 1.813274595Subproblem 2
y + -0.3 = -1.513274595 Simplifying y + -0.3 = -1.513274595 Reorder the terms: -0.3 + y = -1.513274595 Solving -0.3 + y = -1.513274595 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 = -1.513274595 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + y = -1.513274595 + 0.3 y = -1.513274595 + 0.3 Combine like terms: -1.513274595 + 0.3 = -1.213274595 y = -1.213274595 Simplifying y = -1.213274595Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.813274595, -1.213274595}
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