(5x^2-4x-8)+(6x^2-9x+7)=

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Solution for (5x^2-4x-8)+(6x^2-9x+7)= equation:


Simplifying
(5x2 + -4x + -8) + (6x2 + -9x + 7) = 0

Reorder the terms:
(-8 + -4x + 5x2) + (6x2 + -9x + 7) = 0

Remove parenthesis around (-8 + -4x + 5x2)
-8 + -4x + 5x2 + (6x2 + -9x + 7) = 0

Reorder the terms:
-8 + -4x + 5x2 + (7 + -9x + 6x2) = 0

Remove parenthesis around (7 + -9x + 6x2)
-8 + -4x + 5x2 + 7 + -9x + 6x2 = 0

Reorder the terms:
-8 + 7 + -4x + -9x + 5x2 + 6x2 = 0

Combine like terms: -8 + 7 = -1
-1 + -4x + -9x + 5x2 + 6x2 = 0

Combine like terms: -4x + -9x = -13x
-1 + -13x + 5x2 + 6x2 = 0

Combine like terms: 5x2 + 6x2 = 11x2
-1 + -13x + 11x2 = 0

Solving
-1 + -13x + 11x2 = 0

Solving for variable 'x'.

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

Divide each side by '11'.
-0.09090909091 + -1.181818182x + x2 = 0

Move the constant term to the right:

Add '0.09090909091' to each side of the equation.
-0.09090909091 + -1.181818182x + 0.09090909091 + x2 = 0 + 0.09090909091

Reorder the terms:
-0.09090909091 + 0.09090909091 + -1.181818182x + x2 = 0 + 0.09090909091

Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000
0.00000000000 + -1.181818182x + x2 = 0 + 0.09090909091
-1.181818182x + x2 = 0 + 0.09090909091

Combine like terms: 0 + 0.09090909091 = 0.09090909091
-1.181818182x + x2 = 0.09090909091

The x term is -1.181818182x.  Take half its coefficient (-0.590909091).
Square it (0.3491735538) and add it to both sides.

Add '0.3491735538' to each side of the equation.
-1.181818182x + 0.3491735538 + x2 = 0.09090909091 + 0.3491735538

Reorder the terms:
0.3491735538 + -1.181818182x + x2 = 0.09090909091 + 0.3491735538

Combine like terms: 0.09090909091 + 0.3491735538 = 0.44008264471
0.3491735538 + -1.181818182x + x2 = 0.44008264471

Factor a perfect square on the left side:
(x + -0.590909091)(x + -0.590909091) = 0.44008264471

Calculate the square root of the right side: 0.663387251

Break this problem into two subproblems by setting 
(x + -0.590909091) equal to 0.663387251 and -0.663387251.

Subproblem 1

x + -0.590909091 = 0.663387251 Simplifying x + -0.590909091 = 0.663387251 Reorder the terms: -0.590909091 + x = 0.663387251 Solving -0.590909091 + x = 0.663387251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.590909091' to each side of the equation. -0.590909091 + 0.590909091 + x = 0.663387251 + 0.590909091 Combine like terms: -0.590909091 + 0.590909091 = 0.000000000 0.000000000 + x = 0.663387251 + 0.590909091 x = 0.663387251 + 0.590909091 Combine like terms: 0.663387251 + 0.590909091 = 1.254296342 x = 1.254296342 Simplifying x = 1.254296342

Subproblem 2

x + -0.590909091 = -0.663387251 Simplifying x + -0.590909091 = -0.663387251 Reorder the terms: -0.590909091 + x = -0.663387251 Solving -0.590909091 + x = -0.663387251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.590909091' to each side of the equation. -0.590909091 + 0.590909091 + x = -0.663387251 + 0.590909091 Combine like terms: -0.590909091 + 0.590909091 = 0.000000000 0.000000000 + x = -0.663387251 + 0.590909091 x = -0.663387251 + 0.590909091 Combine like terms: -0.663387251 + 0.590909091 = -0.07247816 x = -0.07247816 Simplifying x = -0.07247816

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.254296342, -0.07247816}

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