25x^2-10x+1=27

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Solution for 25x^2-10x+1=27 equation:


Simplifying
25x2 + -10x + 1 = 27

Reorder the terms:
1 + -10x + 25x2 = 27

Solving
1 + -10x + 25x2 = 27

Solving for variable 'x'.

Reorder the terms:
1 + -27 + -10x + 25x2 = 27 + -27

Combine like terms: 1 + -27 = -26
-26 + -10x + 25x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-26 + -10x + 25x2 = 0

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

Divide each side by '25'.
-1.04 + -0.4x + x2 = 0

Move the constant term to the right:

Add '1.04' to each side of the equation.
-1.04 + -0.4x + 1.04 + x2 = 0 + 1.04

Reorder the terms:
-1.04 + 1.04 + -0.4x + x2 = 0 + 1.04

Combine like terms: -1.04 + 1.04 = 0.00
0.00 + -0.4x + x2 = 0 + 1.04
-0.4x + x2 = 0 + 1.04

Combine like terms: 0 + 1.04 = 1.04
-0.4x + x2 = 1.04

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 = 1.04 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 1.04 + 0.04

Combine like terms: 1.04 + 0.04 = 1.08
0.04 + -0.4x + x2 = 1.08

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 1.08

Calculate the square root of the right side: 1.039230485

Break this problem into two subproblems by setting 
(x + -0.2) equal to 1.039230485 and -1.039230485.

Subproblem 1

x + -0.2 = 1.039230485 Simplifying x + -0.2 = 1.039230485 Reorder the terms: -0.2 + x = 1.039230485 Solving -0.2 + x = 1.039230485 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 = 1.039230485 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.039230485 + 0.2 x = 1.039230485 + 0.2 Combine like terms: 1.039230485 + 0.2 = 1.239230485 x = 1.239230485 Simplifying x = 1.239230485

Subproblem 2

x + -0.2 = -1.039230485 Simplifying x + -0.2 = -1.039230485 Reorder the terms: -0.2 + x = -1.039230485 Solving -0.2 + x = -1.039230485 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 = -1.039230485 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.039230485 + 0.2 x = -1.039230485 + 0.2 Combine like terms: -1.039230485 + 0.2 = -0.839230485 x = -0.839230485 Simplifying x = -0.839230485

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.239230485, -0.839230485}

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