5x^2+32x-11=

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Solution for 5x^2+32x-11= equation:


Simplifying
5x2 + 32x + -11 = 0

Reorder the terms:
-11 + 32x + 5x2 = 0

Solving
-11 + 32x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-2.2 + 6.4x + x2 = 0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + 6.4x + 2.2 + x2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + 6.4x + x2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + 6.4x + x2 = 0 + 2.2
6.4x + x2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
6.4x + x2 = 2.2

The x term is 6.4x.  Take half its coefficient (3.2).
Square it (10.24) and add it to both sides.

Add '10.24' to each side of the equation.
6.4x + 10.24 + x2 = 2.2 + 10.24

Reorder the terms:
10.24 + 6.4x + x2 = 2.2 + 10.24

Combine like terms: 2.2 + 10.24 = 12.44
10.24 + 6.4x + x2 = 12.44

Factor a perfect square on the left side:
(x + 3.2)(x + 3.2) = 12.44

Calculate the square root of the right side: 3.527038418

Break this problem into two subproblems by setting 
(x + 3.2) equal to 3.527038418 and -3.527038418.

Subproblem 1

x + 3.2 = 3.527038418 Simplifying x + 3.2 = 3.527038418 Reorder the terms: 3.2 + x = 3.527038418 Solving 3.2 + x = 3.527038418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = 3.527038418 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = 3.527038418 + -3.2 x = 3.527038418 + -3.2 Combine like terms: 3.527038418 + -3.2 = 0.327038418 x = 0.327038418 Simplifying x = 0.327038418

Subproblem 2

x + 3.2 = -3.527038418 Simplifying x + 3.2 = -3.527038418 Reorder the terms: 3.2 + x = -3.527038418 Solving 3.2 + x = -3.527038418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = -3.527038418 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = -3.527038418 + -3.2 x = -3.527038418 + -3.2 Combine like terms: -3.527038418 + -3.2 = -6.727038418 x = -6.727038418 Simplifying x = -6.727038418

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.327038418, -6.727038418}

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