5x(8x-5)=11x+11

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Solution for 5x(8x-5)=11x+11 equation:


Simplifying
5x(8x + -5) = 11x + 11

Reorder the terms:
5x(-5 + 8x) = 11x + 11
(-5 * 5x + 8x * 5x) = 11x + 11
(-25x + 40x2) = 11x + 11

Reorder the terms:
-25x + 40x2 = 11 + 11x

Solving
-25x + 40x2 = 11 + 11x

Solving for variable 'x'.

Reorder the terms:
-11 + -25x + -11x + 40x2 = 11 + 11x + -11 + -11x

Combine like terms: -25x + -11x = -36x
-11 + -36x + 40x2 = 11 + 11x + -11 + -11x

Reorder the terms:
-11 + -36x + 40x2 = 11 + -11 + 11x + -11x

Combine like terms: 11 + -11 = 0
-11 + -36x + 40x2 = 0 + 11x + -11x
-11 + -36x + 40x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
-11 + -36x + 40x2 = 0

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

Divide each side by '40'.
-0.275 + -0.9x + x2 = 0.0

Move the constant term to the right:

Add '0.275' to each side of the equation.
-0.275 + -0.9x + 0.275 + x2 = 0.0 + 0.275

Reorder the terms:
-0.275 + 0.275 + -0.9x + x2 = 0.0 + 0.275

Combine like terms: -0.275 + 0.275 = 0.000
0.000 + -0.9x + x2 = 0.0 + 0.275
-0.9x + x2 = 0.0 + 0.275

Combine like terms: 0.0 + 0.275 = 0.275
-0.9x + x2 = 0.275

The x term is -0.9x.  Take half its coefficient (-0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
-0.9x + 0.2025 + x2 = 0.275 + 0.2025

Reorder the terms:
0.2025 + -0.9x + x2 = 0.275 + 0.2025

Combine like terms: 0.275 + 0.2025 = 0.4775
0.2025 + -0.9x + x2 = 0.4775

Factor a perfect square on the left side:
(x + -0.45)(x + -0.45) = 0.4775

Calculate the square root of the right side: 0.691013748

Break this problem into two subproblems by setting 
(x + -0.45) equal to 0.691013748 and -0.691013748.

Subproblem 1

x + -0.45 = 0.691013748 Simplifying x + -0.45 = 0.691013748 Reorder the terms: -0.45 + x = 0.691013748 Solving -0.45 + x = 0.691013748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = 0.691013748 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = 0.691013748 + 0.45 x = 0.691013748 + 0.45 Combine like terms: 0.691013748 + 0.45 = 1.141013748 x = 1.141013748 Simplifying x = 1.141013748

Subproblem 2

x + -0.45 = -0.691013748 Simplifying x + -0.45 = -0.691013748 Reorder the terms: -0.45 + x = -0.691013748 Solving -0.45 + x = -0.691013748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = -0.691013748 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = -0.691013748 + 0.45 x = -0.691013748 + 0.45 Combine like terms: -0.691013748 + 0.45 = -0.241013748 x = -0.241013748 Simplifying x = -0.241013748

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.141013748, -0.241013748}

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