5x^2+4x-128=0

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Solution for 5x^2+4x-128=0 equation:


Simplifying
5x2 + 4x + -128 = 0

Reorder the terms:
-128 + 4x + 5x2 = 0

Solving
-128 + 4x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-25.6 + 0.8x + x2 = 0

Move the constant term to the right:

Add '25.6' to each side of the equation.
-25.6 + 0.8x + 25.6 + x2 = 0 + 25.6

Reorder the terms:
-25.6 + 25.6 + 0.8x + x2 = 0 + 25.6

Combine like terms: -25.6 + 25.6 = 0.0
0.0 + 0.8x + x2 = 0 + 25.6
0.8x + x2 = 0 + 25.6

Combine like terms: 0 + 25.6 = 25.6
0.8x + x2 = 25.6

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 25.6 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 25.6 + 0.16

Combine like terms: 25.6 + 0.16 = 25.76
0.16 + 0.8x + x2 = 25.76

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 25.76

Calculate the square root of the right side: 5.075431016

Break this problem into two subproblems by setting 
(x + 0.4) equal to 5.075431016 and -5.075431016.

Subproblem 1

x + 0.4 = 5.075431016 Simplifying x + 0.4 = 5.075431016 Reorder the terms: 0.4 + x = 5.075431016 Solving 0.4 + x = 5.075431016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 5.075431016 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 5.075431016 + -0.4 x = 5.075431016 + -0.4 Combine like terms: 5.075431016 + -0.4 = 4.675431016 x = 4.675431016 Simplifying x = 4.675431016

Subproblem 2

x + 0.4 = -5.075431016 Simplifying x + 0.4 = -5.075431016 Reorder the terms: 0.4 + x = -5.075431016 Solving 0.4 + x = -5.075431016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -5.075431016 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -5.075431016 + -0.4 x = -5.075431016 + -0.4 Combine like terms: -5.075431016 + -0.4 = -5.475431016 x = -5.475431016 Simplifying x = -5.475431016

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.675431016, -5.475431016}

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