4x(x-5)=5x^2-6x-5

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Solution for 4x(x-5)=5x^2-6x-5 equation:


Simplifying
4x(x + -5) = 5x2 + -6x + -5

Reorder the terms:
4x(-5 + x) = 5x2 + -6x + -5
(-5 * 4x + x * 4x) = 5x2 + -6x + -5
(-20x + 4x2) = 5x2 + -6x + -5

Reorder the terms:
-20x + 4x2 = -5 + -6x + 5x2

Solving
-20x + 4x2 = -5 + -6x + 5x2

Solving for variable 'x'.

Reorder the terms:
5 + -20x + 6x + 4x2 + -5x2 = -5 + -6x + 5x2 + 5 + 6x + -5x2

Combine like terms: -20x + 6x = -14x
5 + -14x + 4x2 + -5x2 = -5 + -6x + 5x2 + 5 + 6x + -5x2

Combine like terms: 4x2 + -5x2 = -1x2
5 + -14x + -1x2 = -5 + -6x + 5x2 + 5 + 6x + -5x2

Reorder the terms:
5 + -14x + -1x2 = -5 + 5 + -6x + 6x + 5x2 + -5x2

Combine like terms: -5 + 5 = 0
5 + -14x + -1x2 = 0 + -6x + 6x + 5x2 + -5x2
5 + -14x + -1x2 = -6x + 6x + 5x2 + -5x2

Combine like terms: -6x + 6x = 0
5 + -14x + -1x2 = 0 + 5x2 + -5x2
5 + -14x + -1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
5 + -14x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-5 + 14x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 14x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 14x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 14x + x2 = 0 + 5
14x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
14x + x2 = 5

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 5 + 49

Reorder the terms:
49 + 14x + x2 = 5 + 49

Combine like terms: 5 + 49 = 54
49 + 14x + x2 = 54

Factor a perfect square on the left side:
(x + 7)(x + 7) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(x + 7) equal to 7.348469228 and -7.348469228.

Subproblem 1

x + 7 = 7.348469228 Simplifying x + 7 = 7.348469228 Reorder the terms: 7 + x = 7.348469228 Solving 7 + x = 7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 7.348469228 + -7 Combine like terms: 7 + -7 = 0 0 + x = 7.348469228 + -7 x = 7.348469228 + -7 Combine like terms: 7.348469228 + -7 = 0.348469228 x = 0.348469228 Simplifying x = 0.348469228

Subproblem 2

x + 7 = -7.348469228 Simplifying x + 7 = -7.348469228 Reorder the terms: 7 + x = -7.348469228 Solving 7 + x = -7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -7.348469228 + -7 Combine like terms: 7 + -7 = 0 0 + x = -7.348469228 + -7 x = -7.348469228 + -7 Combine like terms: -7.348469228 + -7 = -14.348469228 x = -14.348469228 Simplifying x = -14.348469228

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.348469228, -14.348469228}

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