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Simplifying (y2 + -7y + -5) + -1(-3y2 + 3y + -4) = 0 Reorder the terms: (-5 + -7y + y2) + -1(-3y2 + 3y + -4) = 0 Remove parenthesis around (-5 + -7y + y2) -5 + -7y + y2 + -1(-3y2 + 3y + -4) = 0 Reorder the terms: -5 + -7y + y2 + -1(-4 + 3y + -3y2) = 0 -5 + -7y + y2 + (-4 * -1 + 3y * -1 + -3y2 * -1) = 0 -5 + -7y + y2 + (4 + -3y + 3y2) = 0 Reorder the terms: -5 + 4 + -7y + -3y + y2 + 3y2 = 0 Combine like terms: -5 + 4 = -1 -1 + -7y + -3y + y2 + 3y2 = 0 Combine like terms: -7y + -3y = -10y -1 + -10y + y2 + 3y2 = 0 Combine like terms: y2 + 3y2 = 4y2 -1 + -10y + 4y2 = 0 Solving -1 + -10y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -2.5y + y2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -2.5y + 0.25 + y2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -2.5y + y2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -2.5y + y2 = 0 + 0.25 -2.5y + y2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -2.5y + y2 = 0.25 The y term is -2.5y. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5y + 1.5625 + y2 = 0.25 + 1.5625 Reorder the terms: 1.5625 + -2.5y + y2 = 0.25 + 1.5625 Combine like terms: 0.25 + 1.5625 = 1.8125 1.5625 + -2.5y + y2 = 1.8125 Factor a perfect square on the left side: (y + -1.25)(y + -1.25) = 1.8125 Calculate the square root of the right side: 1.346291202 Break this problem into two subproblems by setting (y + -1.25) equal to 1.346291202 and -1.346291202.Subproblem 1
y + -1.25 = 1.346291202 Simplifying y + -1.25 = 1.346291202 Reorder the terms: -1.25 + y = 1.346291202 Solving -1.25 + y = 1.346291202 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + y = 1.346291202 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + y = 1.346291202 + 1.25 y = 1.346291202 + 1.25 Combine like terms: 1.346291202 + 1.25 = 2.596291202 y = 2.596291202 Simplifying y = 2.596291202Subproblem 2
y + -1.25 = -1.346291202 Simplifying y + -1.25 = -1.346291202 Reorder the terms: -1.25 + y = -1.346291202 Solving -1.25 + y = -1.346291202 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + y = -1.346291202 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + y = -1.346291202 + 1.25 y = -1.346291202 + 1.25 Combine like terms: -1.346291202 + 1.25 = -0.096291202 y = -0.096291202 Simplifying y = -0.096291202Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.596291202, -0.096291202}
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