8x^2=6-7x

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Solution for 8x^2=6-7x equation:


Simplifying
8x2 = 6 + -7x

Solving
8x2 = 6 + -7x

Solving for variable 'x'.

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

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

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

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

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

Divide each side by '8'.
-0.75 + 0.875x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 0.875x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 0.875x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 0.875x + x2 = 0 + 0.75
0.875x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
0.875x + x2 = 0.75

The x term is 0.875x.  Take half its coefficient (0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
0.875x + 0.19140625 + x2 = 0.75 + 0.19140625

Reorder the terms:
0.19140625 + 0.875x + x2 = 0.75 + 0.19140625

Combine like terms: 0.75 + 0.19140625 = 0.94140625
0.19140625 + 0.875x + x2 = 0.94140625

Factor a perfect square on the left side:
(x + 0.4375)(x + 0.4375) = 0.94140625

Calculate the square root of the right side: 0.970260919

Break this problem into two subproblems by setting 
(x + 0.4375) equal to 0.970260919 and -0.970260919.

Subproblem 1

x + 0.4375 = 0.970260919 Simplifying x + 0.4375 = 0.970260919 Reorder the terms: 0.4375 + x = 0.970260919 Solving 0.4375 + x = 0.970260919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = 0.970260919 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = 0.970260919 + -0.4375 x = 0.970260919 + -0.4375 Combine like terms: 0.970260919 + -0.4375 = 0.532760919 x = 0.532760919 Simplifying x = 0.532760919

Subproblem 2

x + 0.4375 = -0.970260919 Simplifying x + 0.4375 = -0.970260919 Reorder the terms: 0.4375 + x = -0.970260919 Solving 0.4375 + x = -0.970260919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = -0.970260919 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = -0.970260919 + -0.4375 x = -0.970260919 + -0.4375 Combine like terms: -0.970260919 + -0.4375 = -1.407760919 x = -1.407760919 Simplifying x = -1.407760919

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.532760919, -1.407760919}

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