-4y^2+17y+5=0

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Solution for -4y^2+17y+5=0 equation:


Simplifying
-4y2 + 17y + 5 = 0

Reorder the terms:
5 + 17y + -4y2 = 0

Solving
5 + 17y + -4y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1.25 + -4.25y + y2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -4.25y + 1.25 + y2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -4.25y + y2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -4.25y + y2 = 0 + 1.25
-4.25y + y2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-4.25y + y2 = 1.25

The y term is -4.25y.  Take half its coefficient (-2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
-4.25y + 4.515625 + y2 = 1.25 + 4.515625

Reorder the terms:
4.515625 + -4.25y + y2 = 1.25 + 4.515625

Combine like terms: 1.25 + 4.515625 = 5.765625
4.515625 + -4.25y + y2 = 5.765625

Factor a perfect square on the left side:
(y + -2.125)(y + -2.125) = 5.765625

Calculate the square root of the right side: 2.401171589

Break this problem into two subproblems by setting 
(y + -2.125) equal to 2.401171589 and -2.401171589.

Subproblem 1

y + -2.125 = 2.401171589 Simplifying y + -2.125 = 2.401171589 Reorder the terms: -2.125 + y = 2.401171589 Solving -2.125 + y = 2.401171589 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + y = 2.401171589 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + y = 2.401171589 + 2.125 y = 2.401171589 + 2.125 Combine like terms: 2.401171589 + 2.125 = 4.526171589 y = 4.526171589 Simplifying y = 4.526171589

Subproblem 2

y + -2.125 = -2.401171589 Simplifying y + -2.125 = -2.401171589 Reorder the terms: -2.125 + y = -2.401171589 Solving -2.125 + y = -2.401171589 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + y = -2.401171589 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + y = -2.401171589 + 2.125 y = -2.401171589 + 2.125 Combine like terms: -2.401171589 + 2.125 = -0.276171589 y = -0.276171589 Simplifying y = -0.276171589

Solution

The solution to the problem is based on the solutions from the subproblems. y = {4.526171589, -0.276171589}

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