4x^2+20x-7=0

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Solution for 4x^2+20x-7=0 equation:


Simplifying
4x2 + 20x + -7 = 0

Reorder the terms:
-7 + 20x + 4x2 = 0

Solving
-7 + 20x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-1.75 + 5x + x2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + 5x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + 5x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + 5x + x2 = 0 + 1.75
5x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
5x + x2 = 1.75

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 = 1.75 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 1.75 + 6.25

Combine like terms: 1.75 + 6.25 = 8
6.25 + 5x + x2 = 8

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.828427125 and -2.828427125.

Subproblem 1

x + 2.5 = 2.828427125 Simplifying x + 2.5 = 2.828427125 Reorder the terms: 2.5 + x = 2.828427125 Solving 2.5 + x = 2.828427125 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 = 2.828427125 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.828427125 + -2.5 x = 2.828427125 + -2.5 Combine like terms: 2.828427125 + -2.5 = 0.328427125 x = 0.328427125 Simplifying x = 0.328427125

Subproblem 2

x + 2.5 = -2.828427125 Simplifying x + 2.5 = -2.828427125 Reorder the terms: 2.5 + x = -2.828427125 Solving 2.5 + x = -2.828427125 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 = -2.828427125 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.828427125 + -2.5 x = -2.828427125 + -2.5 Combine like terms: -2.828427125 + -2.5 = -5.328427125 x = -5.328427125 Simplifying x = -5.328427125

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.328427125, -5.328427125}

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