-4.9x^2+34.3x+1=0

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Solution for -4.9x^2+34.3x+1=0 equation:


Simplifying
-4.9x2 + 34.3x + 1 = 0

Reorder the terms:
1 + 34.3x + -4.9x2 = 0

Solving
1 + 34.3x + -4.9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-0.2040816327 + -7x + x2 = 0

Move the constant term to the right:

Add '0.2040816327' to each side of the equation.
-0.2040816327 + -7x + 0.2040816327 + x2 = 0 + 0.2040816327

Reorder the terms:
-0.2040816327 + 0.2040816327 + -7x + x2 = 0 + 0.2040816327

Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000
0.0000000000 + -7x + x2 = 0 + 0.2040816327
-7x + x2 = 0 + 0.2040816327

Combine like terms: 0 + 0.2040816327 = 0.2040816327
-7x + x2 = 0.2040816327

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 0.2040816327 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 0.2040816327 + 12.25

Combine like terms: 0.2040816327 + 12.25 = 12.4540816327
12.25 + -7x + x2 = 12.4540816327

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 12.4540816327

Calculate the square root of the right side: 3.529034093

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.529034093 and -3.529034093.

Subproblem 1

x + -3.5 = 3.529034093 Simplifying x + -3.5 = 3.529034093 Reorder the terms: -3.5 + x = 3.529034093 Solving -3.5 + x = 3.529034093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.529034093 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.529034093 + 3.5 x = 3.529034093 + 3.5 Combine like terms: 3.529034093 + 3.5 = 7.029034093 x = 7.029034093 Simplifying x = 7.029034093

Subproblem 2

x + -3.5 = -3.529034093 Simplifying x + -3.5 = -3.529034093 Reorder the terms: -3.5 + x = -3.529034093 Solving -3.5 + x = -3.529034093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.529034093 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.529034093 + 3.5 x = -3.529034093 + 3.5 Combine like terms: -3.529034093 + 3.5 = -0.029034093 x = -0.029034093 Simplifying x = -0.029034093

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.029034093, -0.029034093}

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