7X^2+16X=8

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Solution for 7X^2+16X=8 equation:


Simplifying
7X2 + 16X = 8

Reorder the terms:
16X + 7X2 = 8

Solving
16X + 7X2 = 8

Solving for variable 'X'.

Reorder the terms:
-8 + 16X + 7X2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 16X + 7X2 = 0

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

Divide each side by '7'.
-1.142857143 + 2.285714286X + X2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + 2.285714286X + 1.142857143 + X2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + 2.285714286X + X2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + 2.285714286X + X2 = 0 + 1.142857143
2.285714286X + X2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
2.285714286X + X2 = 1.142857143

The X term is 2.285714286X.  Take half its coefficient (1.142857143).
Square it (1.306122449) and add it to both sides.

Add '1.306122449' to each side of the equation.
2.285714286X + 1.306122449 + X2 = 1.142857143 + 1.306122449

Reorder the terms:
1.306122449 + 2.285714286X + X2 = 1.142857143 + 1.306122449

Combine like terms: 1.142857143 + 1.306122449 = 2.448979592
1.306122449 + 2.285714286X + X2 = 2.448979592

Factor a perfect square on the left side:
(X + 1.142857143)(X + 1.142857143) = 2.448979592

Calculate the square root of the right side: 1.564921593

Break this problem into two subproblems by setting 
(X + 1.142857143) equal to 1.564921593 and -1.564921593.

Subproblem 1

X + 1.142857143 = 1.564921593 Simplifying X + 1.142857143 = 1.564921593 Reorder the terms: 1.142857143 + X = 1.564921593 Solving 1.142857143 + X = 1.564921593 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.142857143' to each side of the equation. 1.142857143 + -1.142857143 + X = 1.564921593 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + X = 1.564921593 + -1.142857143 X = 1.564921593 + -1.142857143 Combine like terms: 1.564921593 + -1.142857143 = 0.42206445 X = 0.42206445 Simplifying X = 0.42206445

Subproblem 2

X + 1.142857143 = -1.564921593 Simplifying X + 1.142857143 = -1.564921593 Reorder the terms: 1.142857143 + X = -1.564921593 Solving 1.142857143 + X = -1.564921593 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.142857143' to each side of the equation. 1.142857143 + -1.142857143 + X = -1.564921593 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + X = -1.564921593 + -1.142857143 X = -1.564921593 + -1.142857143 Combine like terms: -1.564921593 + -1.142857143 = -2.707778736 X = -2.707778736 Simplifying X = -2.707778736

Solution

The solution to the problem is based on the solutions from the subproblems. X = {0.42206445, -2.707778736}

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