5x^2-35+2x=0

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Solution for 5x^2-35+2x=0 equation:


Simplifying
5x2 + -35 + 2x = 0

Reorder the terms:
-35 + 2x + 5x2 = 0

Solving
-35 + 2x + 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'.
-7 + 0.4x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 0.4x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 0.4x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 0.4x + x2 = 0 + 7
0.4x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
0.4x + x2 = 7

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 = 7 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 7 + 0.04

Combine like terms: 7 + 0.04 = 7.04
0.04 + 0.4x + x2 = 7.04

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 7.04

Calculate the square root of the right side: 2.653299832

Break this problem into two subproblems by setting 
(x + 0.2) equal to 2.653299832 and -2.653299832.

Subproblem 1

x + 0.2 = 2.653299832 Simplifying x + 0.2 = 2.653299832 Reorder the terms: 0.2 + x = 2.653299832 Solving 0.2 + x = 2.653299832 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 = 2.653299832 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 2.653299832 + -0.2 x = 2.653299832 + -0.2 Combine like terms: 2.653299832 + -0.2 = 2.453299832 x = 2.453299832 Simplifying x = 2.453299832

Subproblem 2

x + 0.2 = -2.653299832 Simplifying x + 0.2 = -2.653299832 Reorder the terms: 0.2 + x = -2.653299832 Solving 0.2 + x = -2.653299832 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 = -2.653299832 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -2.653299832 + -0.2 x = -2.653299832 + -0.2 Combine like terms: -2.653299832 + -0.2 = -2.853299832 x = -2.853299832 Simplifying x = -2.853299832

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.453299832, -2.853299832}

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