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Simplifying 25y2 + 40y + 16 = 28 Reorder the terms: 16 + 40y + 25y2 = 28 Solving 16 + 40y + 25y2 = 28 Solving for variable 'y'. Reorder the terms: 16 + -28 + 40y + 25y2 = 28 + -28 Combine like terms: 16 + -28 = -12 -12 + 40y + 25y2 = 28 + -28 Combine like terms: 28 + -28 = 0 -12 + 40y + 25y2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.48 + 1.6y + y2 = 0 Move the constant term to the right: Add '0.48' to each side of the equation. -0.48 + 1.6y + 0.48 + y2 = 0 + 0.48 Reorder the terms: -0.48 + 0.48 + 1.6y + y2 = 0 + 0.48 Combine like terms: -0.48 + 0.48 = 0.00 0.00 + 1.6y + y2 = 0 + 0.48 1.6y + y2 = 0 + 0.48 Combine like terms: 0 + 0.48 = 0.48 1.6y + y2 = 0.48 The y term is 1.6y. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6y + 0.64 + y2 = 0.48 + 0.64 Reorder the terms: 0.64 + 1.6y + y2 = 0.48 + 0.64 Combine like terms: 0.48 + 0.64 = 1.12 0.64 + 1.6y + y2 = 1.12 Factor a perfect square on the left side: (y + 0.8)(y + 0.8) = 1.12 Calculate the square root of the right side: 1.058300524 Break this problem into two subproblems by setting (y + 0.8) equal to 1.058300524 and -1.058300524.Subproblem 1
y + 0.8 = 1.058300524 Simplifying y + 0.8 = 1.058300524 Reorder the terms: 0.8 + y = 1.058300524 Solving 0.8 + y = 1.058300524 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + y = 1.058300524 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + y = 1.058300524 + -0.8 y = 1.058300524 + -0.8 Combine like terms: 1.058300524 + -0.8 = 0.258300524 y = 0.258300524 Simplifying y = 0.258300524Subproblem 2
y + 0.8 = -1.058300524 Simplifying y + 0.8 = -1.058300524 Reorder the terms: 0.8 + y = -1.058300524 Solving 0.8 + y = -1.058300524 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + y = -1.058300524 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + y = -1.058300524 + -0.8 y = -1.058300524 + -0.8 Combine like terms: -1.058300524 + -0.8 = -1.858300524 y = -1.858300524 Simplifying y = -1.858300524Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.258300524, -1.858300524}
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