25x^2+7x=2x+1

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Solution for 25x^2+7x=2x+1 equation:


Simplifying
25x2 + 7x = 2x + 1

Reorder the terms:
7x + 25x2 = 2x + 1

Reorder the terms:
7x + 25x2 = 1 + 2x

Solving
7x + 25x2 = 1 + 2x

Solving for variable 'x'.

Reorder the terms:
-1 + 7x + -2x + 25x2 = 1 + 2x + -1 + -2x

Combine like terms: 7x + -2x = 5x
-1 + 5x + 25x2 = 1 + 2x + -1 + -2x

Reorder the terms:
-1 + 5x + 25x2 = 1 + -1 + 2x + -2x

Combine like terms: 1 + -1 = 0
-1 + 5x + 25x2 = 0 + 2x + -2x
-1 + 5x + 25x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-1 + 5x + 25x2 = 0

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

Divide each side by '25'.
-0.04 + 0.2x + x2 = 0

Move the constant term to the right:

Add '0.04' to each side of the equation.
-0.04 + 0.2x + 0.04 + x2 = 0 + 0.04

Reorder the terms:
-0.04 + 0.04 + 0.2x + x2 = 0 + 0.04

Combine like terms: -0.04 + 0.04 = 0.00
0.00 + 0.2x + x2 = 0 + 0.04
0.2x + x2 = 0 + 0.04

Combine like terms: 0 + 0.04 = 0.04
0.2x + x2 = 0.04

The x term is 0.2x.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2x + 0.01 + x2 = 0.04 + 0.01

Reorder the terms:
0.01 + 0.2x + x2 = 0.04 + 0.01

Combine like terms: 0.04 + 0.01 = 0.05
0.01 + 0.2x + x2 = 0.05

Factor a perfect square on the left side:
(x + 0.1)(x + 0.1) = 0.05

Calculate the square root of the right side: 0.223606798

Break this problem into two subproblems by setting 
(x + 0.1) equal to 0.223606798 and -0.223606798.

Subproblem 1

x + 0.1 = 0.223606798 Simplifying x + 0.1 = 0.223606798 Reorder the terms: 0.1 + x = 0.223606798 Solving 0.1 + x = 0.223606798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 0.223606798 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.223606798 + -0.1 x = 0.223606798 + -0.1 Combine like terms: 0.223606798 + -0.1 = 0.123606798 x = 0.123606798 Simplifying x = 0.123606798

Subproblem 2

x + 0.1 = -0.223606798 Simplifying x + 0.1 = -0.223606798 Reorder the terms: 0.1 + x = -0.223606798 Solving 0.1 + x = -0.223606798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -0.223606798 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.223606798 + -0.1 x = -0.223606798 + -0.1 Combine like terms: -0.223606798 + -0.1 = -0.323606798 x = -0.323606798 Simplifying x = -0.323606798

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.123606798, -0.323606798}

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