25x^2=20x+6

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Solution for 25x^2=20x+6 equation:


Simplifying
25x2 = 20x + 6

Reorder the terms:
25x2 = 6 + 20x

Solving
25x2 = 6 + 20x

Solving for variable 'x'.

Reorder the terms:
-6 + -20x + 25x2 = 6 + 20x + -6 + -20x

Reorder the terms:
-6 + -20x + 25x2 = 6 + -6 + 20x + -20x

Combine like terms: 6 + -6 = 0
-6 + -20x + 25x2 = 0 + 20x + -20x
-6 + -20x + 25x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
-6 + -20x + 25x2 = 0

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

Divide each side by '25'.
-0.24 + -0.8x + x2 = 0

Move the constant term to the right:

Add '0.24' to each side of the equation.
-0.24 + -0.8x + 0.24 + x2 = 0 + 0.24

Reorder the terms:
-0.24 + 0.24 + -0.8x + x2 = 0 + 0.24

Combine like terms: -0.24 + 0.24 = 0.00
0.00 + -0.8x + x2 = 0 + 0.24
-0.8x + x2 = 0 + 0.24

Combine like terms: 0 + 0.24 = 0.24
-0.8x + x2 = 0.24

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = 0.24 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = 0.24 + 0.16

Combine like terms: 0.24 + 0.16 = 0.4
0.16 + -0.8x + x2 = 0.4

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 0.4

Calculate the square root of the right side: 0.632455532

Break this problem into two subproblems by setting 
(x + -0.4) equal to 0.632455532 and -0.632455532.

Subproblem 1

x + -0.4 = 0.632455532 Simplifying x + -0.4 = 0.632455532 Reorder the terms: -0.4 + x = 0.632455532 Solving -0.4 + x = 0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.632455532 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.632455532 + 0.4 x = 0.632455532 + 0.4 Combine like terms: 0.632455532 + 0.4 = 1.032455532 x = 1.032455532 Simplifying x = 1.032455532

Subproblem 2

x + -0.4 = -0.632455532 Simplifying x + -0.4 = -0.632455532 Reorder the terms: -0.4 + x = -0.632455532 Solving -0.4 + x = -0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -0.632455532 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.632455532 + 0.4 x = -0.632455532 + 0.4 Combine like terms: -0.632455532 + 0.4 = -0.232455532 x = -0.232455532 Simplifying x = -0.232455532

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.032455532, -0.232455532}

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