7(x)(x)-16x=8

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Solution for 7(x)(x)-16x=8 equation:


Simplifying
7(x)(x) + -16x = 8

Multiply x * x
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 = 2.707778736 x = 2.707778736 Simplifying x = 2.707778736

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 = -0.42206445 x = -0.42206445 Simplifying x = -0.42206445

Solution

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

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