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

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


Simplifying
(8x + 8) + -1(7x2 + 5x + 6) = 0

Reorder the terms:
(8 + 8x) + -1(7x2 + 5x + 6) = 0

Remove parenthesis around (8 + 8x)
8 + 8x + -1(7x2 + 5x + 6) = 0

Reorder the terms:
8 + 8x + -1(6 + 5x + 7x2) = 0
8 + 8x + (6 * -1 + 5x * -1 + 7x2 * -1) = 0
8 + 8x + (-6 + -5x + -7x2) = 0

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

Combine like terms: 8 + -6 = 2
2 + 8x + -5x + -7x2 = 0

Combine like terms: 8x + -5x = 3x
2 + 3x + -7x2 = 0

Solving
2 + 3x + -7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-0.2857142857 + -0.4285714286x + x2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + -0.4285714286x + 0.2857142857 + x2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + -0.4285714286x + x2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + -0.4285714286x + x2 = 0 + 0.2857142857
-0.4285714286x + x2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
-0.4285714286x + x2 = 0.2857142857

The x term is -0.4285714286x.  Take half its coefficient (-0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
-0.4285714286x + 0.04591836735 + x2 = 0.2857142857 + 0.04591836735

Reorder the terms:
0.04591836735 + -0.4285714286x + x2 = 0.2857142857 + 0.04591836735

Combine like terms: 0.2857142857 + 0.04591836735 = 0.33163265305
0.04591836735 + -0.4285714286x + x2 = 0.33163265305

Factor a perfect square on the left side:
(x + -0.2142857143)(x + -0.2142857143) = 0.33163265305

Calculate the square root of the right side: 0.575875553

Break this problem into two subproblems by setting 
(x + -0.2142857143) equal to 0.575875553 and -0.575875553.

Subproblem 1

x + -0.2142857143 = 0.575875553 Simplifying x + -0.2142857143 = 0.575875553 Reorder the terms: -0.2142857143 + x = 0.575875553 Solving -0.2142857143 + x = 0.575875553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = 0.575875553 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 0.575875553 + 0.2142857143 x = 0.575875553 + 0.2142857143 Combine like terms: 0.575875553 + 0.2142857143 = 0.7901612673 x = 0.7901612673 Simplifying x = 0.7901612673

Subproblem 2

x + -0.2142857143 = -0.575875553 Simplifying x + -0.2142857143 = -0.575875553 Reorder the terms: -0.2142857143 + x = -0.575875553 Solving -0.2142857143 + x = -0.575875553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = -0.575875553 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -0.575875553 + 0.2142857143 x = -0.575875553 + 0.2142857143 Combine like terms: -0.575875553 + 0.2142857143 = -0.3615898387 x = -0.3615898387 Simplifying x = -0.3615898387

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.7901612673, -0.3615898387}

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