4x(x+30)=(5x-25)

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Solution for 4x(x+30)=(5x-25) equation:


Simplifying
4x(x + 30) = (5x + -25)

Reorder the terms:
4x(30 + x) = (5x + -25)
(30 * 4x + x * 4x) = (5x + -25)
(120x + 4x2) = (5x + -25)

Reorder the terms:
120x + 4x2 = (-25 + 5x)

Remove parenthesis around (-25 + 5x)
120x + 4x2 = -25 + 5x

Solving
120x + 4x2 = -25 + 5x

Solving for variable 'x'.

Reorder the terms:
25 + 120x + -5x + 4x2 = -25 + 5x + 25 + -5x

Combine like terms: 120x + -5x = 115x
25 + 115x + 4x2 = -25 + 5x + 25 + -5x

Reorder the terms:
25 + 115x + 4x2 = -25 + 25 + 5x + -5x

Combine like terms: -25 + 25 = 0
25 + 115x + 4x2 = 0 + 5x + -5x
25 + 115x + 4x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
25 + 115x + 4x2 = 0

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

Divide each side by '4'.
6.25 + 28.75x + x2 = 0

Move the constant term to the right:

Add '-6.25' to each side of the equation.
6.25 + 28.75x + -6.25 + x2 = 0 + -6.25

Reorder the terms:
6.25 + -6.25 + 28.75x + x2 = 0 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + 28.75x + x2 = 0 + -6.25
28.75x + x2 = 0 + -6.25

Combine like terms: 0 + -6.25 = -6.25
28.75x + x2 = -6.25

The x term is 28.75x.  Take half its coefficient (14.375).
Square it (206.640625) and add it to both sides.

Add '206.640625' to each side of the equation.
28.75x + 206.640625 + x2 = -6.25 + 206.640625

Reorder the terms:
206.640625 + 28.75x + x2 = -6.25 + 206.640625

Combine like terms: -6.25 + 206.640625 = 200.390625
206.640625 + 28.75x + x2 = 200.390625

Factor a perfect square on the left side:
(x + 14.375)(x + 14.375) = 200.390625

Calculate the square root of the right side: 14.155939566

Break this problem into two subproblems by setting 
(x + 14.375) equal to 14.155939566 and -14.155939566.

Subproblem 1

x + 14.375 = 14.155939566 Simplifying x + 14.375 = 14.155939566 Reorder the terms: 14.375 + x = 14.155939566 Solving 14.375 + x = 14.155939566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.375' to each side of the equation. 14.375 + -14.375 + x = 14.155939566 + -14.375 Combine like terms: 14.375 + -14.375 = 0.000 0.000 + x = 14.155939566 + -14.375 x = 14.155939566 + -14.375 Combine like terms: 14.155939566 + -14.375 = -0.219060434 x = -0.219060434 Simplifying x = -0.219060434

Subproblem 2

x + 14.375 = -14.155939566 Simplifying x + 14.375 = -14.155939566 Reorder the terms: 14.375 + x = -14.155939566 Solving 14.375 + x = -14.155939566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.375' to each side of the equation. 14.375 + -14.375 + x = -14.155939566 + -14.375 Combine like terms: 14.375 + -14.375 = 0.000 0.000 + x = -14.155939566 + -14.375 x = -14.155939566 + -14.375 Combine like terms: -14.155939566 + -14.375 = -28.530939566 x = -28.530939566 Simplifying x = -28.530939566

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.219060434, -28.530939566}

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