25x^2+10x+1=3

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Solution for 25x^2+10x+1=3 equation:


Simplifying
25x2 + 10x + 1 = 3

Reorder the terms:
1 + 10x + 25x2 = 3

Solving
1 + 10x + 25x2 = 3

Solving for variable 'x'.

Reorder the terms:
1 + -3 + 10x + 25x2 = 3 + -3

Combine like terms: 1 + -3 = -2
-2 + 10x + 25x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-2 + 10x + 25x2 = 0

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

Divide each side by '25'.
-0.08 + 0.4x + x2 = 0

Move the constant term to the right:

Add '0.08' to each side of the equation.
-0.08 + 0.4x + 0.08 + x2 = 0 + 0.08

Reorder the terms:
-0.08 + 0.08 + 0.4x + x2 = 0 + 0.08

Combine like terms: -0.08 + 0.08 = 0.00
0.00 + 0.4x + x2 = 0 + 0.08
0.4x + x2 = 0 + 0.08

Combine like terms: 0 + 0.08 = 0.08
0.4x + x2 = 0.08

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 0.08 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 0.08 + 0.04

Combine like terms: 0.08 + 0.04 = 0.12
0.04 + 0.4x + x2 = 0.12

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 0.12

Calculate the square root of the right side: 0.346410162

Break this problem into two subproblems by setting 
(x + 0.2) equal to 0.346410162 and -0.346410162.

Subproblem 1

x + 0.2 = 0.346410162 Simplifying x + 0.2 = 0.346410162 Reorder the terms: 0.2 + x = 0.346410162 Solving 0.2 + x = 0.346410162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.346410162 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.346410162 + -0.2 x = 0.346410162 + -0.2 Combine like terms: 0.346410162 + -0.2 = 0.146410162 x = 0.146410162 Simplifying x = 0.146410162

Subproblem 2

x + 0.2 = -0.346410162 Simplifying x + 0.2 = -0.346410162 Reorder the terms: 0.2 + x = -0.346410162 Solving 0.2 + x = -0.346410162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.346410162 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.346410162 + -0.2 x = -0.346410162 + -0.2 Combine like terms: -0.346410162 + -0.2 = -0.546410162 x = -0.546410162 Simplifying x = -0.546410162

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.146410162, -0.546410162}

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