4(x-7)-(x+8)-5(3x-5)x=1

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Solution for 4(x-7)-(x+8)-5(3x-5)x=1 equation: 


Simplifying
4(x + -7) + -1(x + 8) + -5(3x + -5) * x = 1

Reorder the terms:
4(-7 + x) + -1(x + 8) + -5(3x + -5) * x = 1
(-7 * 4 + x * 4) + -1(x + 8) + -5(3x + -5) * x = 1
(-28 + 4x) + -1(x + 8) + -5(3x + -5) * x = 1

Reorder the terms:
-28 + 4x + -1(8 + x) + -5(3x + -5) * x = 1
-28 + 4x + (8 * -1 + x * -1) + -5(3x + -5) * x = 1
-28 + 4x + (-8 + -1x) + -5(3x + -5) * x = 1

Reorder the terms:
-28 + 4x + -8 + -1x + -5(-5 + 3x) * x = 1

Reorder the terms for easier multiplication:
-28 + 4x + -8 + -1x + -5x(-5 + 3x) = 1
-28 + 4x + -8 + -1x + (-5 * -5x + 3x * -5x) = 1
-28 + 4x + -8 + -1x + (25x + -15x2) = 1

Reorder the terms:
-28 + -8 + 4x + -1x + 25x + -15x2 = 1

Combine like terms: -28 + -8 = -36
-36 + 4x + -1x + 25x + -15x2 = 1

Combine like terms: 4x + -1x = 3x
-36 + 3x + 25x + -15x2 = 1

Combine like terms: 3x + 25x = 28x
-36 + 28x + -15x2 = 1

Solving
-36 + 28x + -15x2 = 1

Solving for variable 'x'.

Reorder the terms:
-36 + -1 + 28x + -15x2 = 1 + -1

Combine like terms: -36 + -1 = -37
-37 + 28x + -15x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-37 + 28x + -15x2 = 0

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
2.466666667 + -1.866666667x + x2 = 0

Move the constant term to the right:

Add '-2.466666667' to each side of the equation.
2.466666667 + -1.866666667x + -2.466666667 + x2 = 0 + -2.466666667

Reorder the terms:
2.466666667 + -2.466666667 + -1.866666667x + x2 = 0 + -2.466666667

Combine like terms: 2.466666667 + -2.466666667 = 0.000000000
0.000000000 + -1.866666667x + x2 = 0 + -2.466666667
-1.866666667x + x2 = 0 + -2.466666667

Combine like terms: 0 + -2.466666667 = -2.466666667
-1.866666667x + x2 = -2.466666667

The x term is -1.866666667x.  Take half its coefficient (-0.9333333335).
Square it (0.8711111114) and add it to both sides.

Add '0.8711111114' to each side of the equation.
-1.866666667x + 0.8711111114 + x2 = -2.466666667 + 0.8711111114

Reorder the terms:
0.8711111114 + -1.866666667x + x2 = -2.466666667 + 0.8711111114

Combine like terms: -2.466666667 + 0.8711111114 = -1.5955555556
0.8711111114 + -1.866666667x + x2 = -1.5955555556

Factor a perfect square on the left side:
(x + -0.9333333335)(x + -0.9333333335) = -1.5955555556

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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