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Simplifying (9y2 + 9y + -5) + -1(-4y + 7) = 0 Reorder the terms: (-5 + 9y + 9y2) + -1(-4y + 7) = 0 Remove parenthesis around (-5 + 9y + 9y2) -5 + 9y + 9y2 + -1(-4y + 7) = 0 Reorder the terms: -5 + 9y + 9y2 + -1(7 + -4y) = 0 -5 + 9y + 9y2 + (7 * -1 + -4y * -1) = 0 -5 + 9y + 9y2 + (-7 + 4y) = 0 Reorder the terms: -5 + -7 + 9y + 4y + 9y2 = 0 Combine like terms: -5 + -7 = -12 -12 + 9y + 4y + 9y2 = 0 Combine like terms: 9y + 4y = 13y -12 + 13y + 9y2 = 0 Solving -12 + 13y + 9y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.333333333 + 1.444444444y + y2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 1.444444444y + 1.333333333 + y2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 1.444444444y + y2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 1.444444444y + y2 = 0 + 1.333333333 1.444444444y + y2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 1.444444444y + y2 = 1.333333333 The y term is 1.444444444y. Take half its coefficient (0.722222222). Square it (0.5216049380) and add it to both sides. Add '0.5216049380' to each side of the equation. 1.444444444y + 0.5216049380 + y2 = 1.333333333 + 0.5216049380 Reorder the terms: 0.5216049380 + 1.444444444y + y2 = 1.333333333 + 0.5216049380 Combine like terms: 1.333333333 + 0.5216049380 = 1.854938271 0.5216049380 + 1.444444444y + y2 = 1.854938271 Factor a perfect square on the left side: (y + 0.722222222)(y + 0.722222222) = 1.854938271 Calculate the square root of the right side: 1.361961186 Break this problem into two subproblems by setting (y + 0.722222222) equal to 1.361961186 and -1.361961186.Subproblem 1
y + 0.722222222 = 1.361961186 Simplifying y + 0.722222222 = 1.361961186 Reorder the terms: 0.722222222 + y = 1.361961186 Solving 0.722222222 + y = 1.361961186 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.722222222' to each side of the equation. 0.722222222 + -0.722222222 + y = 1.361961186 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + y = 1.361961186 + -0.722222222 y = 1.361961186 + -0.722222222 Combine like terms: 1.361961186 + -0.722222222 = 0.639738964 y = 0.639738964 Simplifying y = 0.639738964Subproblem 2
y + 0.722222222 = -1.361961186 Simplifying y + 0.722222222 = -1.361961186 Reorder the terms: 0.722222222 + y = -1.361961186 Solving 0.722222222 + y = -1.361961186 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.722222222' to each side of the equation. 0.722222222 + -0.722222222 + y = -1.361961186 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + y = -1.361961186 + -0.722222222 y = -1.361961186 + -0.722222222 Combine like terms: -1.361961186 + -0.722222222 = -2.084183408 y = -2.084183408 Simplifying y = -2.084183408Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.639738964, -2.084183408}
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