(5x-1)(5x-1)=43

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Solution for (5x-1)(5x-1)=43 equation:


Simplifying
(5x + -1)(5x + -1) = 43

Reorder the terms:
(-1 + 5x)(5x + -1) = 43

Reorder the terms:
(-1 + 5x)(-1 + 5x) = 43

Multiply (-1 + 5x) * (-1 + 5x)
(-1(-1 + 5x) + 5x * (-1 + 5x)) = 43
((-1 * -1 + 5x * -1) + 5x * (-1 + 5x)) = 43
((1 + -5x) + 5x * (-1 + 5x)) = 43
(1 + -5x + (-1 * 5x + 5x * 5x)) = 43
(1 + -5x + (-5x + 25x2)) = 43

Combine like terms: -5x + -5x = -10x
(1 + -10x + 25x2) = 43

Solving
1 + -10x + 25x2 = 43

Solving for variable 'x'.

Reorder the terms:
1 + -43 + -10x + 25x2 = 43 + -43

Combine like terms: 1 + -43 = -42
-42 + -10x + 25x2 = 43 + -43

Combine like terms: 43 + -43 = 0
-42 + -10x + 25x2 = 0

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

Divide each side by '25'.
-1.68 + -0.4x + x2 = 0

Move the constant term to the right:

Add '1.68' to each side of the equation.
-1.68 + -0.4x + 1.68 + x2 = 0 + 1.68

Reorder the terms:
-1.68 + 1.68 + -0.4x + x2 = 0 + 1.68

Combine like terms: -1.68 + 1.68 = 0.00
0.00 + -0.4x + x2 = 0 + 1.68
-0.4x + x2 = 0 + 1.68

Combine like terms: 0 + 1.68 = 1.68
-0.4x + x2 = 1.68

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 = 1.68 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 1.68 + 0.04

Combine like terms: 1.68 + 0.04 = 1.72
0.04 + -0.4x + x2 = 1.72

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 1.72

Calculate the square root of the right side: 1.311487705

Break this problem into two subproblems by setting 
(x + -0.2) equal to 1.311487705 and -1.311487705.

Subproblem 1

x + -0.2 = 1.311487705 Simplifying x + -0.2 = 1.311487705 Reorder the terms: -0.2 + x = 1.311487705 Solving -0.2 + x = 1.311487705 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 = 1.311487705 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.311487705 + 0.2 x = 1.311487705 + 0.2 Combine like terms: 1.311487705 + 0.2 = 1.511487705 x = 1.511487705 Simplifying x = 1.511487705

Subproblem 2

x + -0.2 = -1.311487705 Simplifying x + -0.2 = -1.311487705 Reorder the terms: -0.2 + x = -1.311487705 Solving -0.2 + x = -1.311487705 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 = -1.311487705 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.311487705 + 0.2 x = -1.311487705 + 0.2 Combine like terms: -1.311487705 + 0.2 = -1.111487705 x = -1.111487705 Simplifying x = -1.111487705

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.511487705, -1.111487705}

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