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Simplifying (-1y2 + 2y + -9) + -1(-5y2 + -2) = 0 Reorder the terms: (-9 + 2y + -1y2) + -1(-5y2 + -2) = 0 Remove parenthesis around (-9 + 2y + -1y2) -9 + 2y + -1y2 + -1(-5y2 + -2) = 0 Reorder the terms: -9 + 2y + -1y2 + -1(-2 + -5y2) = 0 -9 + 2y + -1y2 + (-2 * -1 + -5y2 * -1) = 0 -9 + 2y + -1y2 + (2 + 5y2) = 0 Reorder the terms: -9 + 2 + 2y + -1y2 + 5y2 = 0 Combine like terms: -9 + 2 = -7 -7 + 2y + -1y2 + 5y2 = 0 Combine like terms: -1y2 + 5y2 = 4y2 -7 + 2y + 4y2 = 0 Solving -7 + 2y + 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'. -1.75 + 0.5y + y2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 0.5y + 1.75 + y2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 0.5y + y2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 0.5y + y2 = 0 + 1.75 0.5y + y2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 0.5y + y2 = 1.75 The y term is 0.5y. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5y + 0.0625 + y2 = 1.75 + 0.0625 Reorder the terms: 0.0625 + 0.5y + y2 = 1.75 + 0.0625 Combine like terms: 1.75 + 0.0625 = 1.8125 0.0625 + 0.5y + y2 = 1.8125 Factor a perfect square on the left side: (y + 0.25)(y + 0.25) = 1.8125 Calculate the square root of the right side: 1.346291202 Break this problem into two subproblems by setting (y + 0.25) equal to 1.346291202 and -1.346291202.Subproblem 1
y + 0.25 = 1.346291202 Simplifying y + 0.25 = 1.346291202 Reorder the terms: 0.25 + y = 1.346291202 Solving 0.25 + y = 1.346291202 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + y = 1.346291202 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + y = 1.346291202 + -0.25 y = 1.346291202 + -0.25 Combine like terms: 1.346291202 + -0.25 = 1.096291202 y = 1.096291202 Simplifying y = 1.096291202Subproblem 2
y + 0.25 = -1.346291202 Simplifying y + 0.25 = -1.346291202 Reorder the terms: 0.25 + y = -1.346291202 Solving 0.25 + y = -1.346291202 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + y = -1.346291202 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + y = -1.346291202 + -0.25 y = -1.346291202 + -0.25 Combine like terms: -1.346291202 + -0.25 = -1.596291202 y = -1.596291202 Simplifying y = -1.596291202Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.096291202, -1.596291202}
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