4x^2+8x+5=100

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Solution for 4x^2+8x+5=100 equation:


Simplifying
4x2 + 8x + 5 = 100

Reorder the terms:
5 + 8x + 4x2 = 100

Solving
5 + 8x + 4x2 = 100

Solving for variable 'x'.

Reorder the terms:
5 + -100 + 8x + 4x2 = 100 + -100

Combine like terms: 5 + -100 = -95
-95 + 8x + 4x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-95 + 8x + 4x2 = 0

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

Divide each side by '4'.
-23.75 + 2x + x2 = 0

Move the constant term to the right:

Add '23.75' to each side of the equation.
-23.75 + 2x + 23.75 + x2 = 0 + 23.75

Reorder the terms:
-23.75 + 23.75 + 2x + x2 = 0 + 23.75

Combine like terms: -23.75 + 23.75 = 0.00
0.00 + 2x + x2 = 0 + 23.75
2x + x2 = 0 + 23.75

Combine like terms: 0 + 23.75 = 23.75
2x + x2 = 23.75

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 = 23.75 + 1

Reorder the terms:
1 + 2x + x2 = 23.75 + 1

Combine like terms: 23.75 + 1 = 24.75
1 + 2x + x2 = 24.75

Factor a perfect square on the left side:
(x + 1)(x + 1) = 24.75

Calculate the square root of the right side: 4.974937186

Break this problem into two subproblems by setting 
(x + 1) equal to 4.974937186 and -4.974937186.

Subproblem 1

x + 1 = 4.974937186 Simplifying x + 1 = 4.974937186 Reorder the terms: 1 + x = 4.974937186 Solving 1 + x = 4.974937186 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 = 4.974937186 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.974937186 + -1 x = 4.974937186 + -1 Combine like terms: 4.974937186 + -1 = 3.974937186 x = 3.974937186 Simplifying x = 3.974937186

Subproblem 2

x + 1 = -4.974937186 Simplifying x + 1 = -4.974937186 Reorder the terms: 1 + x = -4.974937186 Solving 1 + x = -4.974937186 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 = -4.974937186 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.974937186 + -1 x = -4.974937186 + -1 Combine like terms: -4.974937186 + -1 = -5.974937186 x = -5.974937186 Simplifying x = -5.974937186

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.974937186, -5.974937186}

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