5x^2+8x=1

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Solution for 5x^2+8x=1 equation:


Simplifying
5x2 + 8x = 1

Reorder the terms:
8x + 5x2 = 1

Solving
8x + 5x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 8x + 5x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 8x + 5x2 = 0

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

Divide each side by '5'.
-0.2 + 1.6x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 1.6x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 1.6x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 1.6x + x2 = 0 + 0.2
1.6x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
1.6x + x2 = 0.2

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = 0.2 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = 0.2 + 0.64

Combine like terms: 0.2 + 0.64 = 0.84
0.64 + 1.6x + x2 = 0.84

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 0.84

Calculate the square root of the right side: 0.916515139

Break this problem into two subproblems by setting 
(x + 0.8) equal to 0.916515139 and -0.916515139.

Subproblem 1

x + 0.8 = 0.916515139 Simplifying x + 0.8 = 0.916515139 Reorder the terms: 0.8 + x = 0.916515139 Solving 0.8 + x = 0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 0.916515139 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 0.916515139 + -0.8 x = 0.916515139 + -0.8 Combine like terms: 0.916515139 + -0.8 = 0.116515139 x = 0.116515139 Simplifying x = 0.116515139

Subproblem 2

x + 0.8 = -0.916515139 Simplifying x + 0.8 = -0.916515139 Reorder the terms: 0.8 + x = -0.916515139 Solving 0.8 + x = -0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -0.916515139 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -0.916515139 + -0.8 x = -0.916515139 + -0.8 Combine like terms: -0.916515139 + -0.8 = -1.716515139 x = -1.716515139 Simplifying x = -1.716515139

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.116515139, -1.716515139}

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