=5x^2+40x-4

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Solution for =5x^2+40x-4 equation:


Simplifying
0 = 5x2 + 40x + -4

Reorder the terms:
0 = -4 + 40x + 5x2

Solving
0 = -4 + 40x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + 4 = 4
4 + -40x + -5x2 = -4 + 40x + 5x2 + 4 + -40x + -5x2

Reorder the terms:
4 + -40x + -5x2 = -4 + 4 + 40x + -40x + 5x2 + -5x2

Combine like terms: -4 + 4 = 0
4 + -40x + -5x2 = 0 + 40x + -40x + 5x2 + -5x2
4 + -40x + -5x2 = 40x + -40x + 5x2 + -5x2

Combine like terms: 40x + -40x = 0
4 + -40x + -5x2 = 0 + 5x2 + -5x2
4 + -40x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
4 + -40x + -5x2 = 0

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

Divide each side by '-5'.
-0.8 + 8x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 8x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 8x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 8x + x2 = 0 + 0.8
8x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
8x + x2 = 0.8

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 0.8 + 16

Reorder the terms:
16 + 8x + x2 = 0.8 + 16

Combine like terms: 0.8 + 16 = 16.8
16 + 8x + x2 = 16.8

Factor a perfect square on the left side:
(x + 4)(x + 4) = 16.8

Calculate the square root of the right side: 4.098780306

Break this problem into two subproblems by setting 
(x + 4) equal to 4.098780306 and -4.098780306.

Subproblem 1

x + 4 = 4.098780306 Simplifying x + 4 = 4.098780306 Reorder the terms: 4 + x = 4.098780306 Solving 4 + x = 4.098780306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.098780306 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.098780306 + -4 x = 4.098780306 + -4 Combine like terms: 4.098780306 + -4 = 0.098780306 x = 0.098780306 Simplifying x = 0.098780306

Subproblem 2

x + 4 = -4.098780306 Simplifying x + 4 = -4.098780306 Reorder the terms: 4 + x = -4.098780306 Solving 4 + x = -4.098780306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.098780306 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.098780306 + -4 x = -4.098780306 + -4 Combine like terms: -4.098780306 + -4 = -8.098780306 x = -8.098780306 Simplifying x = -8.098780306

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.098780306, -8.098780306}

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