(4x-5)x=144

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Solution for (4x-5)x=144 equation:


Simplifying
(4x + -5) * x = 144

Reorder the terms:
(-5 + 4x) * x = 144

Reorder the terms for easier multiplication:
x(-5 + 4x) = 144
(-5 * x + 4x * x) = 144
(-5x + 4x2) = 144

Solving
-5x + 4x2 = 144

Solving for variable 'x'.

Reorder the terms:
-144 + -5x + 4x2 = 144 + -144

Combine like terms: 144 + -144 = 0
-144 + -5x + 4x2 = 0

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

Divide each side by '4'.
-36 + -1.25x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -1.25x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -1.25x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -1.25x + x2 = 0 + 36
-1.25x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-1.25x + x2 = 36

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = 36 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 36 + 0.390625

Combine like terms: 36 + 0.390625 = 36.390625
0.390625 + -1.25x + x2 = 36.390625

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 36.390625

Calculate the square root of the right side: 6.032464256

Break this problem into two subproblems by setting 
(x + -0.625) equal to 6.032464256 and -6.032464256.

Subproblem 1

x + -0.625 = 6.032464256 Simplifying x + -0.625 = 6.032464256 Reorder the terms: -0.625 + x = 6.032464256 Solving -0.625 + x = 6.032464256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 6.032464256 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 6.032464256 + 0.625 x = 6.032464256 + 0.625 Combine like terms: 6.032464256 + 0.625 = 6.657464256 x = 6.657464256 Simplifying x = 6.657464256

Subproblem 2

x + -0.625 = -6.032464256 Simplifying x + -0.625 = -6.032464256 Reorder the terms: -0.625 + x = -6.032464256 Solving -0.625 + x = -6.032464256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -6.032464256 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -6.032464256 + 0.625 x = -6.032464256 + 0.625 Combine like terms: -6.032464256 + 0.625 = -5.407464256 x = -5.407464256 Simplifying x = -5.407464256

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.657464256, -5.407464256}

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