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Simplifying (-1y2 + -3y + -5) + -1(-3y + -7y + 4) = 0 Reorder the terms: (-5 + -3y + -1y2) + -1(-3y + -7y + 4) = 0 Remove parenthesis around (-5 + -3y + -1y2) -5 + -3y + -1y2 + -1(-3y + -7y + 4) = 0 Reorder the terms: -5 + -3y + -1y2 + -1(4 + -3y + -7y) = 0 Combine like terms: -3y + -7y = -10y -5 + -3y + -1y2 + -1(4 + -10y) = 0 -5 + -3y + -1y2 + (4 * -1 + -10y * -1) = 0 -5 + -3y + -1y2 + (-4 + 10y) = 0 Reorder the terms: -5 + -4 + -3y + 10y + -1y2 = 0 Combine like terms: -5 + -4 = -9 -9 + -3y + 10y + -1y2 = 0 Combine like terms: -3y + 10y = 7y -9 + 7y + -1y2 = 0 Solving -9 + 7y + -1y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 9 + -7y + y2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -7y + -9 + y2 = 0 + -9 Reorder the terms: 9 + -9 + -7y + y2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7y + y2 = 0 + -9 -7y + y2 = 0 + -9 Combine like terms: 0 + -9 = -9 -7y + y2 = -9 The y term is -7y. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7y + 12.25 + y2 = -9 + 12.25 Reorder the terms: 12.25 + -7y + y2 = -9 + 12.25 Combine like terms: -9 + 12.25 = 3.25 12.25 + -7y + y2 = 3.25 Factor a perfect square on the left side: (y + -3.5)(y + -3.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (y + -3.5) equal to 1.802775638 and -1.802775638.Subproblem 1
y + -3.5 = 1.802775638 Simplifying y + -3.5 = 1.802775638 Reorder the terms: -3.5 + y = 1.802775638 Solving -3.5 + y = 1.802775638 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = 1.802775638 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = 1.802775638 + 3.5 y = 1.802775638 + 3.5 Combine like terms: 1.802775638 + 3.5 = 5.302775638 y = 5.302775638 Simplifying y = 5.302775638Subproblem 2
y + -3.5 = -1.802775638 Simplifying y + -3.5 = -1.802775638 Reorder the terms: -3.5 + y = -1.802775638 Solving -3.5 + y = -1.802775638 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = -1.802775638 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = -1.802775638 + 3.5 y = -1.802775638 + 3.5 Combine like terms: -1.802775638 + 3.5 = 1.697224362 y = 1.697224362 Simplifying y = 1.697224362Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.302775638, 1.697224362}
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