(25x-2)(5x-3)=125

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Solution for (25x-2)(5x-3)=125 equation:


Simplifying
(25x + -2)(5x + -3) = 125

Reorder the terms:
(-2 + 25x)(5x + -3) = 125

Reorder the terms:
(-2 + 25x)(-3 + 5x) = 125

Multiply (-2 + 25x) * (-3 + 5x)
(-2(-3 + 5x) + 25x * (-3 + 5x)) = 125
((-3 * -2 + 5x * -2) + 25x * (-3 + 5x)) = 125
((6 + -10x) + 25x * (-3 + 5x)) = 125
(6 + -10x + (-3 * 25x + 5x * 25x)) = 125
(6 + -10x + (-75x + 125x2)) = 125

Combine like terms: -10x + -75x = -85x
(6 + -85x + 125x2) = 125

Solving
6 + -85x + 125x2 = 125

Solving for variable 'x'.

Reorder the terms:
6 + -125 + -85x + 125x2 = 125 + -125

Combine like terms: 6 + -125 = -119
-119 + -85x + 125x2 = 125 + -125

Combine like terms: 125 + -125 = 0
-119 + -85x + 125x2 = 0

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

Divide each side by '125'.
-0.952 + -0.68x + x2 = 0

Move the constant term to the right:

Add '0.952' to each side of the equation.
-0.952 + -0.68x + 0.952 + x2 = 0 + 0.952

Reorder the terms:
-0.952 + 0.952 + -0.68x + x2 = 0 + 0.952

Combine like terms: -0.952 + 0.952 = 0.000
0.000 + -0.68x + x2 = 0 + 0.952
-0.68x + x2 = 0 + 0.952

Combine like terms: 0 + 0.952 = 0.952
-0.68x + x2 = 0.952

The x term is -0.68x.  Take half its coefficient (-0.34).
Square it (0.1156) and add it to both sides.

Add '0.1156' to each side of the equation.
-0.68x + 0.1156 + x2 = 0.952 + 0.1156

Reorder the terms:
0.1156 + -0.68x + x2 = 0.952 + 0.1156

Combine like terms: 0.952 + 0.1156 = 1.0676
0.1156 + -0.68x + x2 = 1.0676

Factor a perfect square on the left side:
(x + -0.34)(x + -0.34) = 1.0676

Calculate the square root of the right side: 1.033247308

Break this problem into two subproblems by setting 
(x + -0.34) equal to 1.033247308 and -1.033247308.

Subproblem 1

x + -0.34 = 1.033247308 Simplifying x + -0.34 = 1.033247308 Reorder the terms: -0.34 + x = 1.033247308 Solving -0.34 + x = 1.033247308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.34' to each side of the equation. -0.34 + 0.34 + x = 1.033247308 + 0.34 Combine like terms: -0.34 + 0.34 = 0.00 0.00 + x = 1.033247308 + 0.34 x = 1.033247308 + 0.34 Combine like terms: 1.033247308 + 0.34 = 1.373247308 x = 1.373247308 Simplifying x = 1.373247308

Subproblem 2

x + -0.34 = -1.033247308 Simplifying x + -0.34 = -1.033247308 Reorder the terms: -0.34 + x = -1.033247308 Solving -0.34 + x = -1.033247308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.34' to each side of the equation. -0.34 + 0.34 + x = -1.033247308 + 0.34 Combine like terms: -0.34 + 0.34 = 0.00 0.00 + x = -1.033247308 + 0.34 x = -1.033247308 + 0.34 Combine like terms: -1.033247308 + 0.34 = -0.693247308 x = -0.693247308 Simplifying x = -0.693247308

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.373247308, -0.693247308}

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