5x^2+8x+4=125

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Solution for 5x^2+8x+4=125 equation:


Simplifying
5x2 + 8x + 4 = 125

Reorder the terms:
4 + 8x + 5x2 = 125

Solving
4 + 8x + 5x2 = 125

Solving for variable 'x'.

Reorder the terms:
4 + -125 + 8x + 5x2 = 125 + -125

Combine like terms: 4 + -125 = -121
-121 + 8x + 5x2 = 125 + -125

Combine like terms: 125 + -125 = 0
-121 + 8x + 5x2 = 0

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

Divide each side by '5'.
-24.2 + 1.6x + x2 = 0

Move the constant term to the right:

Add '24.2' to each side of the equation.
-24.2 + 1.6x + 24.2 + x2 = 0 + 24.2

Reorder the terms:
-24.2 + 24.2 + 1.6x + x2 = 0 + 24.2

Combine like terms: -24.2 + 24.2 = 0.0
0.0 + 1.6x + x2 = 0 + 24.2
1.6x + x2 = 0 + 24.2

Combine like terms: 0 + 24.2 = 24.2
1.6x + x2 = 24.2

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = 24.2 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = 24.2 + 0.64

Combine like terms: 24.2 + 0.64 = 24.84
0.64 + 1.6x + x2 = 24.84

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 24.84

Calculate the square root of the right side: 4.983974318

Break this problem into two subproblems by setting 
(x + 0.8) equal to 4.983974318 and -4.983974318.

Subproblem 1

x + 0.8 = 4.983974318 Simplifying x + 0.8 = 4.983974318 Reorder the terms: 0.8 + x = 4.983974318 Solving 0.8 + x = 4.983974318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 4.983974318 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 4.983974318 + -0.8 x = 4.983974318 + -0.8 Combine like terms: 4.983974318 + -0.8 = 4.183974318 x = 4.183974318 Simplifying x = 4.183974318

Subproblem 2

x + 0.8 = -4.983974318 Simplifying x + 0.8 = -4.983974318 Reorder the terms: 0.8 + x = -4.983974318 Solving 0.8 + x = -4.983974318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -4.983974318 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -4.983974318 + -0.8 x = -4.983974318 + -0.8 Combine like terms: -4.983974318 + -0.8 = -5.783974318 x = -5.783974318 Simplifying x = -5.783974318

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.183974318, -5.783974318}

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