8x^2+31x=98

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Solution for 8x^2+31x=98 equation:


Simplifying
8x2 + 31x = 98

Reorder the terms:
31x + 8x2 = 98

Solving
31x + 8x2 = 98

Solving for variable 'x'.

Reorder the terms:
-98 + 31x + 8x2 = 98 + -98

Combine like terms: 98 + -98 = 0
-98 + 31x + 8x2 = 0

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

Divide each side by '8'.
-12.25 + 3.875x + x2 = 0

Move the constant term to the right:

Add '12.25' to each side of the equation.
-12.25 + 3.875x + 12.25 + x2 = 0 + 12.25

Reorder the terms:
-12.25 + 12.25 + 3.875x + x2 = 0 + 12.25

Combine like terms: -12.25 + 12.25 = 0.00
0.00 + 3.875x + x2 = 0 + 12.25
3.875x + x2 = 0 + 12.25

Combine like terms: 0 + 12.25 = 12.25
3.875x + x2 = 12.25

The x term is 3.875x.  Take half its coefficient (1.9375).
Square it (3.75390625) and add it to both sides.

Add '3.75390625' to each side of the equation.
3.875x + 3.75390625 + x2 = 12.25 + 3.75390625

Reorder the terms:
3.75390625 + 3.875x + x2 = 12.25 + 3.75390625

Combine like terms: 12.25 + 3.75390625 = 16.00390625
3.75390625 + 3.875x + x2 = 16.00390625

Factor a perfect square on the left side:
(x + 1.9375)(x + 1.9375) = 16.00390625

Calculate the square root of the right side: 4.000488251

Break this problem into two subproblems by setting 
(x + 1.9375) equal to 4.000488251 and -4.000488251.

Subproblem 1

x + 1.9375 = 4.000488251 Simplifying x + 1.9375 = 4.000488251 Reorder the terms: 1.9375 + x = 4.000488251 Solving 1.9375 + x = 4.000488251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9375' to each side of the equation. 1.9375 + -1.9375 + x = 4.000488251 + -1.9375 Combine like terms: 1.9375 + -1.9375 = 0.0000 0.0000 + x = 4.000488251 + -1.9375 x = 4.000488251 + -1.9375 Combine like terms: 4.000488251 + -1.9375 = 2.062988251 x = 2.062988251 Simplifying x = 2.062988251

Subproblem 2

x + 1.9375 = -4.000488251 Simplifying x + 1.9375 = -4.000488251 Reorder the terms: 1.9375 + x = -4.000488251 Solving 1.9375 + x = -4.000488251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9375' to each side of the equation. 1.9375 + -1.9375 + x = -4.000488251 + -1.9375 Combine like terms: 1.9375 + -1.9375 = 0.0000 0.0000 + x = -4.000488251 + -1.9375 x = -4.000488251 + -1.9375 Combine like terms: -4.000488251 + -1.9375 = -5.937988251 x = -5.937988251 Simplifying x = -5.937988251

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.062988251, -5.937988251}

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