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Simplifying 80y + 16 = 4y2 + 100 Reorder the terms: 16 + 80y = 4y2 + 100 Reorder the terms: 16 + 80y = 100 + 4y2 Solving 16 + 80y = 100 + 4y2 Solving for variable 'y'. Reorder the terms: 16 + -100 + 80y + -4y2 = 100 + 4y2 + -100 + -4y2 Combine like terms: 16 + -100 = -84 -84 + 80y + -4y2 = 100 + 4y2 + -100 + -4y2 Reorder the terms: -84 + 80y + -4y2 = 100 + -100 + 4y2 + -4y2 Combine like terms: 100 + -100 = 0 -84 + 80y + -4y2 = 0 + 4y2 + -4y2 -84 + 80y + -4y2 = 4y2 + -4y2 Combine like terms: 4y2 + -4y2 = 0 -84 + 80y + -4y2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-21 + 20y + -1y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-21 + 20y + -1y2)' equal to zero and attempt to solve: Simplifying -21 + 20y + -1y2 = 0 Solving -21 + 20y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 21 + -20y + y2 = 0 Move the constant term to the right: Add '-21' to each side of the equation. 21 + -20y + -21 + y2 = 0 + -21 Reorder the terms: 21 + -21 + -20y + y2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -20y + y2 = 0 + -21 -20y + y2 = 0 + -21 Combine like terms: 0 + -21 = -21 -20y + y2 = -21 The y term is -20y. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20y + 100 + y2 = -21 + 100 Reorder the terms: 100 + -20y + y2 = -21 + 100 Combine like terms: -21 + 100 = 79 100 + -20y + y2 = 79 Factor a perfect square on the left side: (y + -10)(y + -10) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (y + -10) equal to 8.888194417 and -8.888194417.Subproblem 1
y + -10 = 8.888194417 Simplifying y + -10 = 8.888194417 Reorder the terms: -10 + y = 8.888194417 Solving -10 + y = 8.888194417 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = 8.888194417 + 10 Combine like terms: -10 + 10 = 0 0 + y = 8.888194417 + 10 y = 8.888194417 + 10 Combine like terms: 8.888194417 + 10 = 18.888194417 y = 18.888194417 Simplifying y = 18.888194417Subproblem 2
y + -10 = -8.888194417 Simplifying y + -10 = -8.888194417 Reorder the terms: -10 + y = -8.888194417 Solving -10 + y = -8.888194417 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = -8.888194417 + 10 Combine like terms: -10 + 10 = 0 0 + y = -8.888194417 + 10 y = -8.888194417 + 10 Combine like terms: -8.888194417 + 10 = 1.111805583 y = 1.111805583 Simplifying y = 1.111805583Solution
The solution to the problem is based on the solutions from the subproblems. y = {18.888194417, 1.111805583}Solution
y = {18.888194417, 1.111805583}
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