4x^2=-20x-19

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Solution for 4x^2=-20x-19 equation:


Simplifying
4x2 = -20x + -19

Reorder the terms:
4x2 = -19 + -20x

Solving
4x2 = -19 + -20x

Solving for variable 'x'.

Reorder the terms:
19 + 20x + 4x2 = -19 + -20x + 19 + 20x

Reorder the terms:
19 + 20x + 4x2 = -19 + 19 + -20x + 20x

Combine like terms: -19 + 19 = 0
19 + 20x + 4x2 = 0 + -20x + 20x
19 + 20x + 4x2 = -20x + 20x

Combine like terms: -20x + 20x = 0
19 + 20x + 4x2 = 0

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

Divide each side by '4'.
4.75 + 5x + x2 = 0

Move the constant term to the right:

Add '-4.75' to each side of the equation.
4.75 + 5x + -4.75 + x2 = 0 + -4.75

Reorder the terms:
4.75 + -4.75 + 5x + x2 = 0 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + 5x + x2 = 0 + -4.75
5x + x2 = 0 + -4.75

Combine like terms: 0 + -4.75 = -4.75
5x + x2 = -4.75

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -4.75 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -4.75 + 6.25

Combine like terms: -4.75 + 6.25 = 1.5
6.25 + 5x + x2 = 1.5

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(x + 2.5) equal to 1.224744871 and -1.224744871.

Subproblem 1

x + 2.5 = 1.224744871 Simplifying x + 2.5 = 1.224744871 Reorder the terms: 2.5 + x = 1.224744871 Solving 2.5 + x = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 1.224744871 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.224744871 + -2.5 x = 1.224744871 + -2.5 Combine like terms: 1.224744871 + -2.5 = -1.275255129 x = -1.275255129 Simplifying x = -1.275255129

Subproblem 2

x + 2.5 = -1.224744871 Simplifying x + 2.5 = -1.224744871 Reorder the terms: 2.5 + x = -1.224744871 Solving 2.5 + x = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -1.224744871 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.224744871 + -2.5 x = -1.224744871 + -2.5 Combine like terms: -1.224744871 + -2.5 = -3.724744871 x = -3.724744871 Simplifying x = -3.724744871

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.275255129, -3.724744871}

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