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Simplifying y = y2 + -625 + 4y + -100 + 15 Reorder the terms: y = -625 + -100 + 15 + 4y + y2 Combine like terms: -625 + -100 = -725 y = -725 + 15 + 4y + y2 Combine like terms: -725 + 15 = -710 y = -710 + 4y + y2 Solving y = -710 + 4y + y2 Solving for variable 'y'. Reorder the terms: 710 + y + -4y + -1y2 = -710 + 4y + y2 + 710 + -4y + -1y2 Combine like terms: y + -4y = -3y 710 + -3y + -1y2 = -710 + 4y + y2 + 710 + -4y + -1y2 Reorder the terms: 710 + -3y + -1y2 = -710 + 710 + 4y + -4y + y2 + -1y2 Combine like terms: -710 + 710 = 0 710 + -3y + -1y2 = 0 + 4y + -4y + y2 + -1y2 710 + -3y + -1y2 = 4y + -4y + y2 + -1y2 Combine like terms: 4y + -4y = 0 710 + -3y + -1y2 = 0 + y2 + -1y2 710 + -3y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 710 + -3y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -710 + 3y + y2 = 0 Move the constant term to the right: Add '710' to each side of the equation. -710 + 3y + 710 + y2 = 0 + 710 Reorder the terms: -710 + 710 + 3y + y2 = 0 + 710 Combine like terms: -710 + 710 = 0 0 + 3y + y2 = 0 + 710 3y + y2 = 0 + 710 Combine like terms: 0 + 710 = 710 3y + y2 = 710 The y term is 3y. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3y + 2.25 + y2 = 710 + 2.25 Reorder the terms: 2.25 + 3y + y2 = 710 + 2.25 Combine like terms: 710 + 2.25 = 712.25 2.25 + 3y + y2 = 712.25 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = 712.25 Calculate the square root of the right side: 26.68801229 Break this problem into two subproblems by setting (y + 1.5) equal to 26.68801229 and -26.68801229.Subproblem 1
y + 1.5 = 26.68801229 Simplifying y + 1.5 = 26.68801229 Reorder the terms: 1.5 + y = 26.68801229 Solving 1.5 + y = 26.68801229 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = 26.68801229 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 26.68801229 + -1.5 y = 26.68801229 + -1.5 Combine like terms: 26.68801229 + -1.5 = 25.18801229 y = 25.18801229 Simplifying y = 25.18801229Subproblem 2
y + 1.5 = -26.68801229 Simplifying y + 1.5 = -26.68801229 Reorder the terms: 1.5 + y = -26.68801229 Solving 1.5 + y = -26.68801229 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = -26.68801229 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -26.68801229 + -1.5 y = -26.68801229 + -1.5 Combine like terms: -26.68801229 + -1.5 = -28.18801229 y = -28.18801229 Simplifying y = -28.18801229Solution
The solution to the problem is based on the solutions from the subproblems. y = {25.18801229, -28.18801229}
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