(8x+7)-(2x^2-5x-5)=

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Solution for (8x+7)-(2x^2-5x-5)= equation:


Simplifying
(8x + 7) + -1(2x2 + -5x + -5) = 0

Reorder the terms:
(7 + 8x) + -1(2x2 + -5x + -5) = 0

Remove parenthesis around (7 + 8x)
7 + 8x + -1(2x2 + -5x + -5) = 0

Reorder the terms:
7 + 8x + -1(-5 + -5x + 2x2) = 0
7 + 8x + (-5 * -1 + -5x * -1 + 2x2 * -1) = 0
7 + 8x + (5 + 5x + -2x2) = 0

Reorder the terms:
7 + 5 + 8x + 5x + -2x2 = 0

Combine like terms: 7 + 5 = 12
12 + 8x + 5x + -2x2 = 0

Combine like terms: 8x + 5x = 13x
12 + 13x + -2x2 = 0

Solving
12 + 13x + -2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-6 + -6.5x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -6.5x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -6.5x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -6.5x + x2 = 0 + 6
-6.5x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-6.5x + x2 = 6

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = 6 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 6 + 10.5625

Combine like terms: 6 + 10.5625 = 16.5625
10.5625 + -6.5x + x2 = 16.5625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 16.5625

Calculate the square root of the right side: 4.069705149

Break this problem into two subproblems by setting 
(x + -3.25) equal to 4.069705149 and -4.069705149.

Subproblem 1

x + -3.25 = 4.069705149 Simplifying x + -3.25 = 4.069705149 Reorder the terms: -3.25 + x = 4.069705149 Solving -3.25 + x = 4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 4.069705149 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 4.069705149 + 3.25 x = 4.069705149 + 3.25 Combine like terms: 4.069705149 + 3.25 = 7.319705149 x = 7.319705149 Simplifying x = 7.319705149

Subproblem 2

x + -3.25 = -4.069705149 Simplifying x + -3.25 = -4.069705149 Reorder the terms: -3.25 + x = -4.069705149 Solving -3.25 + x = -4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -4.069705149 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -4.069705149 + 3.25 x = -4.069705149 + 3.25 Combine like terms: -4.069705149 + 3.25 = -0.819705149 x = -0.819705149 Simplifying x = -0.819705149

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.319705149, -0.819705149}

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