-4.9x^2+34.3x+8=0

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Solution for -4.9x^2+34.3x+8=0 equation:


Simplifying
-4.9x2 + 34.3x + 8 = 0

Reorder the terms:
8 + 34.3x + -4.9x2 = 0

Solving
8 + 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'.
-1.632653061 + -7x + x2 = 0

Move the constant term to the right:

Add '1.632653061' to each side of the equation.
-1.632653061 + -7x + 1.632653061 + x2 = 0 + 1.632653061

Reorder the terms:
-1.632653061 + 1.632653061 + -7x + x2 = 0 + 1.632653061

Combine like terms: -1.632653061 + 1.632653061 = 0.000000000
0.000000000 + -7x + x2 = 0 + 1.632653061
-7x + x2 = 0 + 1.632653061

Combine like terms: 0 + 1.632653061 = 1.632653061
-7x + x2 = 1.632653061

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 = 1.632653061 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 1.632653061 + 12.25

Combine like terms: 1.632653061 + 12.25 = 13.882653061
12.25 + -7x + x2 = 13.882653061

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 13.882653061

Calculate the square root of the right side: 3.725943244

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.725943244 and -3.725943244.

Subproblem 1

x + -3.5 = 3.725943244 Simplifying x + -3.5 = 3.725943244 Reorder the terms: -3.5 + x = 3.725943244 Solving -3.5 + x = 3.725943244 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 = 3.725943244 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.725943244 + 3.5 x = 3.725943244 + 3.5 Combine like terms: 3.725943244 + 3.5 = 7.225943244 x = 7.225943244 Simplifying x = 7.225943244

Subproblem 2

x + -3.5 = -3.725943244 Simplifying x + -3.5 = -3.725943244 Reorder the terms: -3.5 + x = -3.725943244 Solving -3.5 + x = -3.725943244 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 = -3.725943244 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.725943244 + 3.5 x = -3.725943244 + 3.5 Combine like terms: -3.725943244 + 3.5 = -0.225943244 x = -0.225943244 Simplifying x = -0.225943244

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.225943244, -0.225943244}

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