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Simplifying 25y2 + 10y + 10y + 4 = 112 Reorder the terms: 4 + 10y + 10y + 25y2 = 112 Combine like terms: 10y + 10y = 20y 4 + 20y + 25y2 = 112 Solving 4 + 20y + 25y2 = 112 Solving for variable 'y'. Reorder the terms: 4 + -112 + 20y + 25y2 = 112 + -112 Combine like terms: 4 + -112 = -108 -108 + 20y + 25y2 = 112 + -112 Combine like terms: 112 + -112 = 0 -108 + 20y + 25y2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -4.32 + 0.8y + y2 = 0 Move the constant term to the right: Add '4.32' to each side of the equation. -4.32 + 0.8y + 4.32 + y2 = 0 + 4.32 Reorder the terms: -4.32 + 4.32 + 0.8y + y2 = 0 + 4.32 Combine like terms: -4.32 + 4.32 = 0.00 0.00 + 0.8y + y2 = 0 + 4.32 0.8y + y2 = 0 + 4.32 Combine like terms: 0 + 4.32 = 4.32 0.8y + y2 = 4.32 The y term is 0.8y. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8y + 0.16 + y2 = 4.32 + 0.16 Reorder the terms: 0.16 + 0.8y + y2 = 4.32 + 0.16 Combine like terms: 4.32 + 0.16 = 4.48 0.16 + 0.8y + y2 = 4.48 Factor a perfect square on the left side: (y + 0.4)(y + 0.4) = 4.48 Calculate the square root of the right side: 2.116601049 Break this problem into two subproblems by setting (y + 0.4) equal to 2.116601049 and -2.116601049.Subproblem 1
y + 0.4 = 2.116601049 Simplifying y + 0.4 = 2.116601049 Reorder the terms: 0.4 + y = 2.116601049 Solving 0.4 + y = 2.116601049 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + y = 2.116601049 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = 2.116601049 + -0.4 y = 2.116601049 + -0.4 Combine like terms: 2.116601049 + -0.4 = 1.716601049 y = 1.716601049 Simplifying y = 1.716601049Subproblem 2
y + 0.4 = -2.116601049 Simplifying y + 0.4 = -2.116601049 Reorder the terms: 0.4 + y = -2.116601049 Solving 0.4 + y = -2.116601049 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + y = -2.116601049 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = -2.116601049 + -0.4 y = -2.116601049 + -0.4 Combine like terms: -2.116601049 + -0.4 = -2.516601049 y = -2.516601049 Simplifying y = -2.516601049Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.716601049, -2.516601049}
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