4y^2+4y-7=0

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Solution for 4y^2+4y-7=0 equation:


Simplifying
4y2 + 4y + -7 = 0

Reorder the terms:
-7 + 4y + 4y2 = 0

Solving
-7 + 4y + 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'.
-1.75 + y + y2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + y + 1.75 + y2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + y + y2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + y + y2 = 0 + 1.75
y + y2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
y + y2 = 1.75

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + y2 = 1.75 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + y2 = 1.75 + 0.25

Combine like terms: 1.75 + 0.25 = 2
1.25 + y2 = 2

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(y + 0.5) equal to 1.414213562 and -1.414213562.

Subproblem 1

y + 0.5 = 1.414213562 Simplifying y + 0.5 = 1.414213562 Reorder the terms: 0.5 + y = 1.414213562 Solving 0.5 + y = 1.414213562 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 1.414213562 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 1.414213562 + -0.5 y = 1.414213562 + -0.5 Combine like terms: 1.414213562 + -0.5 = 0.914213562 y = 0.914213562 Simplifying y = 0.914213562

Subproblem 2

y + 0.5 = -1.414213562 Simplifying y + 0.5 = -1.414213562 Reorder the terms: 0.5 + y = -1.414213562 Solving 0.5 + y = -1.414213562 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -1.414213562 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -1.414213562 + -0.5 y = -1.414213562 + -0.5 Combine like terms: -1.414213562 + -0.5 = -1.914213562 y = -1.914213562 Simplifying y = -1.914213562

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.914213562, -1.914213562}

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