2x^2+4x+1=90

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Solution for 2x^2+4x+1=90 equation:


Simplifying
2x2 + 4x + 1 = 90

Reorder the terms:
1 + 4x + 2x2 = 90

Solving
1 + 4x + 2x2 = 90

Solving for variable 'x'.

Reorder the terms:
1 + -90 + 4x + 2x2 = 90 + -90

Combine like terms: 1 + -90 = -89
-89 + 4x + 2x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-89 + 4x + 2x2 = 0

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

Divide each side by '2'.
-44.5 + 2x + x2 = 0

Move the constant term to the right:

Add '44.5' to each side of the equation.
-44.5 + 2x + 44.5 + x2 = 0 + 44.5

Reorder the terms:
-44.5 + 44.5 + 2x + x2 = 0 + 44.5

Combine like terms: -44.5 + 44.5 = 0.0
0.0 + 2x + x2 = 0 + 44.5
2x + x2 = 0 + 44.5

Combine like terms: 0 + 44.5 = 44.5
2x + x2 = 44.5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 44.5 + 1

Reorder the terms:
1 + 2x + x2 = 44.5 + 1

Combine like terms: 44.5 + 1 = 45.5
1 + 2x + x2 = 45.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 45.5

Calculate the square root of the right side: 6.745368782

Break this problem into two subproblems by setting 
(x + 1) equal to 6.745368782 and -6.745368782.

Subproblem 1

x + 1 = 6.745368782 Simplifying x + 1 = 6.745368782 Reorder the terms: 1 + x = 6.745368782 Solving 1 + x = 6.745368782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 6.745368782 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.745368782 + -1 x = 6.745368782 + -1 Combine like terms: 6.745368782 + -1 = 5.745368782 x = 5.745368782 Simplifying x = 5.745368782

Subproblem 2

x + 1 = -6.745368782 Simplifying x + 1 = -6.745368782 Reorder the terms: 1 + x = -6.745368782 Solving 1 + x = -6.745368782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -6.745368782 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.745368782 + -1 x = -6.745368782 + -1 Combine like terms: -6.745368782 + -1 = -7.745368782 x = -7.745368782 Simplifying x = -7.745368782

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.745368782, -7.745368782}

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