-8+7x+7x^2=0

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Solution for -8+7x+7x^2=0 equation:


Simplifying
-8 + 7x + 7x2 = 0

Solving
-8 + 7x + 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'.
-1.142857143 + x + x2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + x + 1.142857143 + x2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + x + x2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + x + x2 = 0 + 1.142857143
x + x2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
x + x2 = 1.142857143

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 1.142857143 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 1.142857143 + 0.25

Combine like terms: 1.142857143 + 0.25 = 1.392857143
1.25 + x2 = 1.392857143

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.392857143

Calculate the square root of the right side: 1.180193689

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.180193689 and -1.180193689.

Subproblem 1

x + 0.5 = 1.180193689 Simplifying x + 0.5 = 1.180193689 Reorder the terms: 0.5 + x = 1.180193689 Solving 0.5 + x = 1.180193689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.180193689 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.180193689 + -0.5 x = 1.180193689 + -0.5 Combine like terms: 1.180193689 + -0.5 = 0.680193689 x = 0.680193689 Simplifying x = 0.680193689

Subproblem 2

x + 0.5 = -1.180193689 Simplifying x + 0.5 = -1.180193689 Reorder the terms: 0.5 + x = -1.180193689 Solving 0.5 + x = -1.180193689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.180193689 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.180193689 + -0.5 x = -1.180193689 + -0.5 Combine like terms: -1.180193689 + -0.5 = -1.680193689 x = -1.680193689 Simplifying x = -1.680193689

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.680193689, -1.680193689}

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