4x^2+32x=-23

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Solution for 4x^2+32x=-23 equation:


Simplifying
4x2 + 32x = -23

Reorder the terms:
32x + 4x2 = -23

Solving
32x + 4x2 = -23

Solving for variable 'x'.

Reorder the terms:
23 + 32x + 4x2 = -23 + 23

Combine like terms: -23 + 23 = 0
23 + 32x + 4x2 = 0

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

Divide each side by '4'.
5.75 + 8x + x2 = 0

Move the constant term to the right:

Add '-5.75' to each side of the equation.
5.75 + 8x + -5.75 + x2 = 0 + -5.75

Reorder the terms:
5.75 + -5.75 + 8x + x2 = 0 + -5.75

Combine like terms: 5.75 + -5.75 = 0.00
0.00 + 8x + x2 = 0 + -5.75
8x + x2 = 0 + -5.75

Combine like terms: 0 + -5.75 = -5.75
8x + x2 = -5.75

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -5.75 + 16

Reorder the terms:
16 + 8x + x2 = -5.75 + 16

Combine like terms: -5.75 + 16 = 10.25
16 + 8x + x2 = 10.25

Factor a perfect square on the left side:
(x + 4)(x + 4) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + 4) equal to 3.201562119 and -3.201562119.

Subproblem 1

x + 4 = 3.201562119 Simplifying x + 4 = 3.201562119 Reorder the terms: 4 + x = 3.201562119 Solving 4 + x = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.201562119 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.201562119 + -4 x = 3.201562119 + -4 Combine like terms: 3.201562119 + -4 = -0.798437881 x = -0.798437881 Simplifying x = -0.798437881

Subproblem 2

x + 4 = -3.201562119 Simplifying x + 4 = -3.201562119 Reorder the terms: 4 + x = -3.201562119 Solving 4 + x = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.201562119 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.201562119 + -4 x = -3.201562119 + -4 Combine like terms: -3.201562119 + -4 = -7.201562119 x = -7.201562119 Simplifying x = -7.201562119

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.798437881, -7.201562119}

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