4x^2+8x=91

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Solution for 4x^2+8x=91 equation:


Simplifying
4x2 + 8x = 91

Reorder the terms:
8x + 4x2 = 91

Solving
8x + 4x2 = 91

Solving for variable 'x'.

Reorder the terms:
-91 + 8x + 4x2 = 91 + -91

Combine like terms: 91 + -91 = 0
-91 + 8x + 4x2 = 0

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

Divide each side by '4'.
-22.75 + 2x + x2 = 0

Move the constant term to the right:

Add '22.75' to each side of the equation.
-22.75 + 2x + 22.75 + x2 = 0 + 22.75

Reorder the terms:
-22.75 + 22.75 + 2x + x2 = 0 + 22.75

Combine like terms: -22.75 + 22.75 = 0.00
0.00 + 2x + x2 = 0 + 22.75
2x + x2 = 0 + 22.75

Combine like terms: 0 + 22.75 = 22.75
2x + x2 = 22.75

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 22.75 + 1

Reorder the terms:
1 + 2x + x2 = 22.75 + 1

Combine like terms: 22.75 + 1 = 23.75
1 + 2x + x2 = 23.75

Factor a perfect square on the left side:
(x + 1)(x + 1) = 23.75

Calculate the square root of the right side: 4.873397172

Break this problem into two subproblems by setting 
(x + 1) equal to 4.873397172 and -4.873397172.

Subproblem 1

x + 1 = 4.873397172 Simplifying x + 1 = 4.873397172 Reorder the terms: 1 + x = 4.873397172 Solving 1 + x = 4.873397172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.873397172 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.873397172 + -1 x = 4.873397172 + -1 Combine like terms: 4.873397172 + -1 = 3.873397172 x = 3.873397172 Simplifying x = 3.873397172

Subproblem 2

x + 1 = -4.873397172 Simplifying x + 1 = -4.873397172 Reorder the terms: 1 + x = -4.873397172 Solving 1 + x = -4.873397172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.873397172 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.873397172 + -1 x = -4.873397172 + -1 Combine like terms: -4.873397172 + -1 = -5.873397172 x = -5.873397172 Simplifying x = -5.873397172

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.873397172, -5.873397172}

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