29x^2+70x-4=0

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Solution for 29x^2+70x-4=0 equation:


Simplifying
29x2 + 70x + -4 = 0

Reorder the terms:
-4 + 70x + 29x2 = 0

Solving
-4 + 70x + 29x2 = 0

Solving for variable 'x'.

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

Divide each side by '29'.
-0.1379310345 + 2.413793103x + x2 = 0

Move the constant term to the right:

Add '0.1379310345' to each side of the equation.
-0.1379310345 + 2.413793103x + 0.1379310345 + x2 = 0 + 0.1379310345

Reorder the terms:
-0.1379310345 + 0.1379310345 + 2.413793103x + x2 = 0 + 0.1379310345

Combine like terms: -0.1379310345 + 0.1379310345 = 0.0000000000
0.0000000000 + 2.413793103x + x2 = 0 + 0.1379310345
2.413793103x + x2 = 0 + 0.1379310345

Combine like terms: 0 + 0.1379310345 = 0.1379310345
2.413793103x + x2 = 0.1379310345

The x term is 2.413793103x.  Take half its coefficient (1.206896552).
Square it (1.456599287) and add it to both sides.

Add '1.456599287' to each side of the equation.
2.413793103x + 1.456599287 + x2 = 0.1379310345 + 1.456599287

Reorder the terms:
1.456599287 + 2.413793103x + x2 = 0.1379310345 + 1.456599287

Combine like terms: 0.1379310345 + 1.456599287 = 1.5945303215
1.456599287 + 2.413793103x + x2 = 1.5945303215

Factor a perfect square on the left side:
(x + 1.206896552)(x + 1.206896552) = 1.5945303215

Calculate the square root of the right side: 1.262747133

Break this problem into two subproblems by setting 
(x + 1.206896552) equal to 1.262747133 and -1.262747133.

Subproblem 1

x + 1.206896552 = 1.262747133 Simplifying x + 1.206896552 = 1.262747133 Reorder the terms: 1.206896552 + x = 1.262747133 Solving 1.206896552 + x = 1.262747133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.206896552' to each side of the equation. 1.206896552 + -1.206896552 + x = 1.262747133 + -1.206896552 Combine like terms: 1.206896552 + -1.206896552 = 0.000000000 0.000000000 + x = 1.262747133 + -1.206896552 x = 1.262747133 + -1.206896552 Combine like terms: 1.262747133 + -1.206896552 = 0.055850581 x = 0.055850581 Simplifying x = 0.055850581

Subproblem 2

x + 1.206896552 = -1.262747133 Simplifying x + 1.206896552 = -1.262747133 Reorder the terms: 1.206896552 + x = -1.262747133 Solving 1.206896552 + x = -1.262747133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.206896552' to each side of the equation. 1.206896552 + -1.206896552 + x = -1.262747133 + -1.206896552 Combine like terms: 1.206896552 + -1.206896552 = 0.000000000 0.000000000 + x = -1.262747133 + -1.206896552 x = -1.262747133 + -1.206896552 Combine like terms: -1.262747133 + -1.206896552 = -2.469643685 x = -2.469643685 Simplifying x = -2.469643685

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.055850581, -2.469643685}

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