5x^2+2x=400

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Solution for 5x^2+2x=400 equation:


Simplifying
5x2 + 2x = 400

Reorder the terms:
2x + 5x2 = 400

Solving
2x + 5x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + 2x + 5x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + 2x + 5x2 = 0

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

Divide each side by '5'.
-80 + 0.4x + x2 = 0

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + 0.4x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + 0.4x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + 0.4x + x2 = 0 + 80
0.4x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
0.4x + x2 = 80

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 80 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 80 + 0.04

Combine like terms: 80 + 0.04 = 80.04
0.04 + 0.4x + x2 = 80.04

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 80.04

Calculate the square root of the right side: 8.946507699

Break this problem into two subproblems by setting 
(x + 0.2) equal to 8.946507699 and -8.946507699.

Subproblem 1

x + 0.2 = 8.946507699 Simplifying x + 0.2 = 8.946507699 Reorder the terms: 0.2 + x = 8.946507699 Solving 0.2 + x = 8.946507699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 8.946507699 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 8.946507699 + -0.2 x = 8.946507699 + -0.2 Combine like terms: 8.946507699 + -0.2 = 8.746507699 x = 8.746507699 Simplifying x = 8.746507699

Subproblem 2

x + 0.2 = -8.946507699 Simplifying x + 0.2 = -8.946507699 Reorder the terms: 0.2 + x = -8.946507699 Solving 0.2 + x = -8.946507699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -8.946507699 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -8.946507699 + -0.2 x = -8.946507699 + -0.2 Combine like terms: -8.946507699 + -0.2 = -9.146507699 x = -9.146507699 Simplifying x = -9.146507699

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.746507699, -9.146507699}

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