(8x+1)*(-5x+9)=x

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Solution for (8x+1)*(-5x+9)=x equation:


Simplifying
(8x + 1)(-5x + 9) = x

Reorder the terms:
(1 + 8x)(-5x + 9) = x

Reorder the terms:
(1 + 8x)(9 + -5x) = x

Multiply (1 + 8x) * (9 + -5x)
(1(9 + -5x) + 8x * (9 + -5x)) = x
((9 * 1 + -5x * 1) + 8x * (9 + -5x)) = x
((9 + -5x) + 8x * (9 + -5x)) = x
(9 + -5x + (9 * 8x + -5x * 8x)) = x
(9 + -5x + (72x + -40x2)) = x

Combine like terms: -5x + 72x = 67x
(9 + 67x + -40x2) = x

Solving
9 + 67x + -40x2 = x

Solving for variable 'x'.

Reorder the terms:
9 + 67x + -1x + -40x2 = x + -1x

Combine like terms: 67x + -1x = 66x
9 + 66x + -40x2 = x + -1x

Combine like terms: x + -1x = 0
9 + 66x + -40x2 = 0

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

Divide each side by '-40'.
-0.225 + -1.65x + x2 = 0.0

Move the constant term to the right:

Add '0.225' to each side of the equation.
-0.225 + -1.65x + 0.225 + x2 = 0.0 + 0.225

Reorder the terms:
-0.225 + 0.225 + -1.65x + x2 = 0.0 + 0.225

Combine like terms: -0.225 + 0.225 = 0.000
0.000 + -1.65x + x2 = 0.0 + 0.225
-1.65x + x2 = 0.0 + 0.225

Combine like terms: 0.0 + 0.225 = 0.225
-1.65x + x2 = 0.225

The x term is -1.65x.  Take half its coefficient (-0.825).
Square it (0.680625) and add it to both sides.

Add '0.680625' to each side of the equation.
-1.65x + 0.680625 + x2 = 0.225 + 0.680625

Reorder the terms:
0.680625 + -1.65x + x2 = 0.225 + 0.680625

Combine like terms: 0.225 + 0.680625 = 0.905625
0.680625 + -1.65x + x2 = 0.905625

Factor a perfect square on the left side:
(x + -0.825)(x + -0.825) = 0.905625

Calculate the square root of the right side: 0.951643316

Break this problem into two subproblems by setting 
(x + -0.825) equal to 0.951643316 and -0.951643316.

Subproblem 1

x + -0.825 = 0.951643316 Simplifying x + -0.825 = 0.951643316 Reorder the terms: -0.825 + x = 0.951643316 Solving -0.825 + x = 0.951643316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.825' to each side of the equation. -0.825 + 0.825 + x = 0.951643316 + 0.825 Combine like terms: -0.825 + 0.825 = 0.000 0.000 + x = 0.951643316 + 0.825 x = 0.951643316 + 0.825 Combine like terms: 0.951643316 + 0.825 = 1.776643316 x = 1.776643316 Simplifying x = 1.776643316

Subproblem 2

x + -0.825 = -0.951643316 Simplifying x + -0.825 = -0.951643316 Reorder the terms: -0.825 + x = -0.951643316 Solving -0.825 + x = -0.951643316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.825' to each side of the equation. -0.825 + 0.825 + x = -0.951643316 + 0.825 Combine like terms: -0.825 + 0.825 = 0.000 0.000 + x = -0.951643316 + 0.825 x = -0.951643316 + 0.825 Combine like terms: -0.951643316 + 0.825 = -0.126643316 x = -0.126643316 Simplifying x = -0.126643316

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.776643316, -0.126643316}

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