(5x+4)(x-20)=62-(x-2)

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Solution for (5x+4)(x-20)=62-(x-2) equation:


Simplifying
(5x + 4)(x + -20) = 62 + -1(x + -2)

Reorder the terms:
(4 + 5x)(x + -20) = 62 + -1(x + -2)

Reorder the terms:
(4 + 5x)(-20 + x) = 62 + -1(x + -2)

Multiply (4 + 5x) * (-20 + x)
(4(-20 + x) + 5x * (-20 + x)) = 62 + -1(x + -2)
((-20 * 4 + x * 4) + 5x * (-20 + x)) = 62 + -1(x + -2)
((-80 + 4x) + 5x * (-20 + x)) = 62 + -1(x + -2)
(-80 + 4x + (-20 * 5x + x * 5x)) = 62 + -1(x + -2)
(-80 + 4x + (-100x + 5x2)) = 62 + -1(x + -2)

Combine like terms: 4x + -100x = -96x
(-80 + -96x + 5x2) = 62 + -1(x + -2)

Reorder the terms:
-80 + -96x + 5x2 = 62 + -1(-2 + x)
-80 + -96x + 5x2 = 62 + (-2 * -1 + x * -1)
-80 + -96x + 5x2 = 62 + (2 + -1x)

Combine like terms: 62 + 2 = 64
-80 + -96x + 5x2 = 64 + -1x

Solving
-80 + -96x + 5x2 = 64 + -1x

Solving for variable 'x'.

Reorder the terms:
-80 + -64 + -96x + x + 5x2 = 64 + -1x + -64 + x

Combine like terms: -80 + -64 = -144
-144 + -96x + x + 5x2 = 64 + -1x + -64 + x

Combine like terms: -96x + x = -95x
-144 + -95x + 5x2 = 64 + -1x + -64 + x

Reorder the terms:
-144 + -95x + 5x2 = 64 + -64 + -1x + x

Combine like terms: 64 + -64 = 0
-144 + -95x + 5x2 = 0 + -1x + x
-144 + -95x + 5x2 = -1x + x

Combine like terms: -1x + x = 0
-144 + -95x + 5x2 = 0

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

Divide each side by '5'.
-28.8 + -19x + x2 = 0

Move the constant term to the right:

Add '28.8' to each side of the equation.
-28.8 + -19x + 28.8 + x2 = 0 + 28.8

Reorder the terms:
-28.8 + 28.8 + -19x + x2 = 0 + 28.8

Combine like terms: -28.8 + 28.8 = 0.0
0.0 + -19x + x2 = 0 + 28.8
-19x + x2 = 0 + 28.8

Combine like terms: 0 + 28.8 = 28.8
-19x + x2 = 28.8

The x term is -19x.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19x + 90.25 + x2 = 28.8 + 90.25

Reorder the terms:
90.25 + -19x + x2 = 28.8 + 90.25

Combine like terms: 28.8 + 90.25 = 119.05
90.25 + -19x + x2 = 119.05

Factor a perfect square on the left side:
(x + -9.5)(x + -9.5) = 119.05

Calculate the square root of the right side: 10.91100362

Break this problem into two subproblems by setting 
(x + -9.5) equal to 10.91100362 and -10.91100362.

Subproblem 1

x + -9.5 = 10.91100362 Simplifying x + -9.5 = 10.91100362 Reorder the terms: -9.5 + x = 10.91100362 Solving -9.5 + x = 10.91100362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 10.91100362 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 10.91100362 + 9.5 x = 10.91100362 + 9.5 Combine like terms: 10.91100362 + 9.5 = 20.41100362 x = 20.41100362 Simplifying x = 20.41100362

Subproblem 2

x + -9.5 = -10.91100362 Simplifying x + -9.5 = -10.91100362 Reorder the terms: -9.5 + x = -10.91100362 Solving -9.5 + x = -10.91100362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -10.91100362 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -10.91100362 + 9.5 x = -10.91100362 + 9.5 Combine like terms: -10.91100362 + 9.5 = -1.41100362 x = -1.41100362 Simplifying x = -1.41100362

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.41100362, -1.41100362}

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