4x(5x+4)=155

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Solution for 4x(5x+4)=155 equation:


Simplifying
4x(5x + 4) = 155

Reorder the terms:
4x(4 + 5x) = 155
(4 * 4x + 5x * 4x) = 155
(16x + 20x2) = 155

Solving
16x + 20x2 = 155

Solving for variable 'x'.

Reorder the terms:
-155 + 16x + 20x2 = 155 + -155

Combine like terms: 155 + -155 = 0
-155 + 16x + 20x2 = 0

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

Divide each side by '20'.
-7.75 + 0.8x + x2 = 0.0

Move the constant term to the right:

Add '7.75' to each side of the equation.
-7.75 + 0.8x + 7.75 + x2 = 0.0 + 7.75

Reorder the terms:
-7.75 + 7.75 + 0.8x + x2 = 0.0 + 7.75

Combine like terms: -7.75 + 7.75 = 0.00
0.00 + 0.8x + x2 = 0.0 + 7.75
0.8x + x2 = 0.0 + 7.75

Combine like terms: 0.0 + 7.75 = 7.75
0.8x + x2 = 7.75

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 7.75 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 7.75 + 0.16

Combine like terms: 7.75 + 0.16 = 7.91
0.16 + 0.8x + x2 = 7.91

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 7.91

Calculate the square root of the right side: 2.812472222

Break this problem into two subproblems by setting 
(x + 0.4) equal to 2.812472222 and -2.812472222.

Subproblem 1

x + 0.4 = 2.812472222 Simplifying x + 0.4 = 2.812472222 Reorder the terms: 0.4 + x = 2.812472222 Solving 0.4 + x = 2.812472222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 2.812472222 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 2.812472222 + -0.4 x = 2.812472222 + -0.4 Combine like terms: 2.812472222 + -0.4 = 2.412472222 x = 2.412472222 Simplifying x = 2.412472222

Subproblem 2

x + 0.4 = -2.812472222 Simplifying x + 0.4 = -2.812472222 Reorder the terms: 0.4 + x = -2.812472222 Solving 0.4 + x = -2.812472222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -2.812472222 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -2.812472222 + -0.4 x = -2.812472222 + -0.4 Combine like terms: -2.812472222 + -0.4 = -3.212472222 x = -3.212472222 Simplifying x = -3.212472222

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.412472222, -3.212472222}

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