(5x)(5x-7)=24

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Solution for (5x)(5x-7)=24 equation: 


Simplifying
(5x)(5x + -7) = 24

Remove parenthesis around (5x)
5x(5x + -7) = 24

Reorder the terms:
5x(-7 + 5x) = 24
(-7 * 5x + 5x * 5x) = 24
(-35x + 25x2) = 24

Solving
-35x + 25x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + -35x + 25x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -35x + 25x2 = 0

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

Divide each side by '25'.
-0.96 + -1.4x + x2 = 0

Move the constant term to the right:

Add '0.96' to each side of the equation.
-0.96 + -1.4x + 0.96 + x2 = 0 + 0.96

Reorder the terms:
-0.96 + 0.96 + -1.4x + x2 = 0 + 0.96

Combine like terms: -0.96 + 0.96 = 0.00
0.00 + -1.4x + x2 = 0 + 0.96
-1.4x + x2 = 0 + 0.96

Combine like terms: 0 + 0.96 = 0.96
-1.4x + x2 = 0.96

The x term is -1.4x.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = 0.96 + 0.49

Reorder the terms:
0.49 + -1.4x + x2 = 0.96 + 0.49

Combine like terms: 0.96 + 0.49 = 1.45
0.49 + -1.4x + x2 = 1.45

Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = 1.45

Calculate the square root of the right side: 1.204159458

Break this problem into two subproblems by setting 
(x + -0.7) equal to 1.204159458 and -1.204159458.


Subproblem 1
x + -0.7 = 1.204159458

Simplifying
x + -0.7 = 1.204159458

Reorder the terms:
-0.7 + x = 1.204159458

Solving
-0.7 + x = 1.204159458

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = 1.204159458 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = 1.204159458 + 0.7
x = 1.204159458 + 0.7

Combine like terms: 1.204159458 + 0.7 = 1.904159458
x = 1.904159458

Simplifying
x = 1.904159458


Subproblem 2
x + -0.7 = -1.204159458

Simplifying
x + -0.7 = -1.204159458

Reorder the terms:
-0.7 + x = -1.204159458

Solving
-0.7 + x = -1.204159458

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = -1.204159458 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = -1.204159458 + 0.7
x = -1.204159458 + 0.7

Combine like terms: -1.204159458 + 0.7 = -0.504159458
x = -0.504159458

Simplifying
x = -0.504159458


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.904159458, -0.504159458}

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