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Simplifying 25y2 + 104y + 25 = 0 Reorder the terms: 25 + 104y + 25y2 = 0 Solving 25 + 104y + 25y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 1 + 4.16y + y2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 4.16y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + 4.16y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4.16y + y2 = 0 + -1 4.16y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 4.16y + y2 = -1 The y term is 4.16y. Take half its coefficient (2.08). Square it (4.3264) and add it to both sides. Add '4.3264' to each side of the equation. 4.16y + 4.3264 + y2 = -1 + 4.3264 Reorder the terms: 4.3264 + 4.16y + y2 = -1 + 4.3264 Combine like terms: -1 + 4.3264 = 3.3264 4.3264 + 4.16y + y2 = 3.3264 Factor a perfect square on the left side: (y + 2.08)(y + 2.08) = 3.3264 Calculate the square root of the right side: 1.823842098 Break this problem into two subproblems by setting (y + 2.08) equal to 1.823842098 and -1.823842098.Subproblem 1
y + 2.08 = 1.823842098 Simplifying y + 2.08 = 1.823842098 Reorder the terms: 2.08 + y = 1.823842098 Solving 2.08 + y = 1.823842098 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.08' to each side of the equation. 2.08 + -2.08 + y = 1.823842098 + -2.08 Combine like terms: 2.08 + -2.08 = 0.00 0.00 + y = 1.823842098 + -2.08 y = 1.823842098 + -2.08 Combine like terms: 1.823842098 + -2.08 = -0.256157902 y = -0.256157902 Simplifying y = -0.256157902Subproblem 2
y + 2.08 = -1.823842098 Simplifying y + 2.08 = -1.823842098 Reorder the terms: 2.08 + y = -1.823842098 Solving 2.08 + y = -1.823842098 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.08' to each side of the equation. 2.08 + -2.08 + y = -1.823842098 + -2.08 Combine like terms: 2.08 + -2.08 = 0.00 0.00 + y = -1.823842098 + -2.08 y = -1.823842098 + -2.08 Combine like terms: -1.823842098 + -2.08 = -3.903842098 y = -3.903842098 Simplifying y = -3.903842098Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.256157902, -3.903842098}
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