4u^2+9u=2

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Solution for 4u^2+9u=2 equation:


Simplifying
4u2 + 9u = 2

Reorder the terms:
9u + 4u2 = 2

Solving
9u + 4u2 = 2

Solving for variable 'u'.

Reorder the terms:
-2 + 9u + 4u2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 9u + 4u2 = 0

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

Divide each side by '4'.
-0.5 + 2.25u + u2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 2.25u + 0.5 + u2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 2.25u + u2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 2.25u + u2 = 0 + 0.5
2.25u + u2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
2.25u + u2 = 0.5

The u term is 2.25u.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25u + 1.265625 + u2 = 0.5 + 1.265625

Reorder the terms:
1.265625 + 2.25u + u2 = 0.5 + 1.265625

Combine like terms: 0.5 + 1.265625 = 1.765625
1.265625 + 2.25u + u2 = 1.765625

Factor a perfect square on the left side:
(u + 1.125)(u + 1.125) = 1.765625

Calculate the square root of the right side: 1.328768227

Break this problem into two subproblems by setting 
(u + 1.125) equal to 1.328768227 and -1.328768227.

Subproblem 1

u + 1.125 = 1.328768227 Simplifying u + 1.125 = 1.328768227 Reorder the terms: 1.125 + u = 1.328768227 Solving 1.125 + u = 1.328768227 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + u = 1.328768227 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + u = 1.328768227 + -1.125 u = 1.328768227 + -1.125 Combine like terms: 1.328768227 + -1.125 = 0.203768227 u = 0.203768227 Simplifying u = 0.203768227

Subproblem 2

u + 1.125 = -1.328768227 Simplifying u + 1.125 = -1.328768227 Reorder the terms: 1.125 + u = -1.328768227 Solving 1.125 + u = -1.328768227 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + u = -1.328768227 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + u = -1.328768227 + -1.125 u = -1.328768227 + -1.125 Combine like terms: -1.328768227 + -1.125 = -2.453768227 u = -2.453768227 Simplifying u = -2.453768227

Solution

The solution to the problem is based on the solutions from the subproblems. u = {0.203768227, -2.453768227}

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