5(x-4)+3x-9x=6-(2x+5)8x

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Solution for 5(x-4)+3x-9x=6-(2x+5)8x equation:


Simplifying
5(x + -4) + 3x + -9x = 6 + -1(2x + 5) * 8x

Reorder the terms:
5(-4 + x) + 3x + -9x = 6 + -1(2x + 5) * 8x
(-4 * 5 + x * 5) + 3x + -9x = 6 + -1(2x + 5) * 8x
(-20 + 5x) + 3x + -9x = 6 + -1(2x + 5) * 8x

Combine like terms: 5x + 3x = 8x
-20 + 8x + -9x = 6 + -1(2x + 5) * 8x

Combine like terms: 8x + -9x = -1x
-20 + -1x = 6 + -1(2x + 5) * 8x

Reorder the terms:
-20 + -1x = 6 + -1(5 + 2x) * 8x

Reorder the terms for easier multiplication:
-20 + -1x = 6 + -1 * 8x(5 + 2x)

Multiply -1 * 8
-20 + -1x = 6 + -8x(5 + 2x)
-20 + -1x = 6 + (5 * -8x + 2x * -8x)
-20 + -1x = 6 + (-40x + -16x2)

Solving
-20 + -1x = 6 + -40x + -16x2

Solving for variable 'x'.

Reorder the terms:
-20 + -6 + -1x + 40x + 16x2 = 6 + -40x + -16x2 + -6 + 40x + 16x2

Combine like terms: -20 + -6 = -26
-26 + -1x + 40x + 16x2 = 6 + -40x + -16x2 + -6 + 40x + 16x2

Combine like terms: -1x + 40x = 39x
-26 + 39x + 16x2 = 6 + -40x + -16x2 + -6 + 40x + 16x2

Reorder the terms:
-26 + 39x + 16x2 = 6 + -6 + -40x + 40x + -16x2 + 16x2

Combine like terms: 6 + -6 = 0
-26 + 39x + 16x2 = 0 + -40x + 40x + -16x2 + 16x2
-26 + 39x + 16x2 = -40x + 40x + -16x2 + 16x2

Combine like terms: -40x + 40x = 0
-26 + 39x + 16x2 = 0 + -16x2 + 16x2
-26 + 39x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-26 + 39x + 16x2 = 0

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

Divide each side by '16'.
-1.625 + 2.4375x + x2 = 0

Move the constant term to the right:

Add '1.625' to each side of the equation.
-1.625 + 2.4375x + 1.625 + x2 = 0 + 1.625

Reorder the terms:
-1.625 + 1.625 + 2.4375x + x2 = 0 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + 2.4375x + x2 = 0 + 1.625
2.4375x + x2 = 0 + 1.625

Combine like terms: 0 + 1.625 = 1.625
2.4375x + x2 = 1.625

The x term is 2.4375x.  Take half its coefficient (1.21875).
Square it (1.485351563) and add it to both sides.

Add '1.485351563' to each side of the equation.
2.4375x + 1.485351563 + x2 = 1.625 + 1.485351563

Reorder the terms:
1.485351563 + 2.4375x + x2 = 1.625 + 1.485351563

Combine like terms: 1.625 + 1.485351563 = 3.110351563
1.485351563 + 2.4375x + x2 = 3.110351563

Factor a perfect square on the left side:
(x + 1.21875)(x + 1.21875) = 3.110351563

Calculate the square root of the right side: 1.763618883

Break this problem into two subproblems by setting 
(x + 1.21875) equal to 1.763618883 and -1.763618883.

Subproblem 1

x + 1.21875 = 1.763618883 Simplifying x + 1.21875 = 1.763618883 Reorder the terms: 1.21875 + x = 1.763618883 Solving 1.21875 + x = 1.763618883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.21875' to each side of the equation. 1.21875 + -1.21875 + x = 1.763618883 + -1.21875 Combine like terms: 1.21875 + -1.21875 = 0.00000 0.00000 + x = 1.763618883 + -1.21875 x = 1.763618883 + -1.21875 Combine like terms: 1.763618883 + -1.21875 = 0.544868883 x = 0.544868883 Simplifying x = 0.544868883

Subproblem 2

x + 1.21875 = -1.763618883 Simplifying x + 1.21875 = -1.763618883 Reorder the terms: 1.21875 + x = -1.763618883 Solving 1.21875 + x = -1.763618883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.21875' to each side of the equation. 1.21875 + -1.21875 + x = -1.763618883 + -1.21875 Combine like terms: 1.21875 + -1.21875 = 0.00000 0.00000 + x = -1.763618883 + -1.21875 x = -1.763618883 + -1.21875 Combine like terms: -1.763618883 + -1.21875 = -2.982368883 x = -2.982368883 Simplifying x = -2.982368883

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.544868883, -2.982368883}

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