3.41x^2-x-7(3.41)=0

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Solution for 3.41x^2-x-7(3.41)=0 equation:


Simplifying
3.41x2 + -1x + -7(3.41) = 0

Multiply -7 * 3.41
3.41x2 + -1x + -23.87 = 0

Reorder the terms:
-23.87 + -1x + 3.41x2 = 0

Solving
-23.87 + -1x + 3.41x2 = 0

Solving for variable 'x'.

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

Divide each side by '3.41'.
-7 + -0.293255132x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -0.293255132x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -0.293255132x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -0.293255132x + x2 = 0 + 7
-0.293255132x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-0.293255132x + x2 = 7

The x term is -0.293255132x.  Take half its coefficient (-0.146627566).
Square it (0.02149964311) and add it to both sides.

Add '0.02149964311' to each side of the equation.
-0.293255132x + 0.02149964311 + x2 = 7 + 0.02149964311

Reorder the terms:
0.02149964311 + -0.293255132x + x2 = 7 + 0.02149964311

Combine like terms: 7 + 0.02149964311 = 7.02149964311
0.02149964311 + -0.293255132x + x2 = 7.02149964311

Factor a perfect square on the left side:
(x + -0.146627566)(x + -0.146627566) = 7.02149964311

Calculate the square root of the right side: 2.649811247

Break this problem into two subproblems by setting 
(x + -0.146627566) equal to 2.649811247 and -2.649811247.

Subproblem 1

x + -0.146627566 = 2.649811247 Simplifying x + -0.146627566 = 2.649811247 Reorder the terms: -0.146627566 + x = 2.649811247 Solving -0.146627566 + x = 2.649811247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.146627566' to each side of the equation. -0.146627566 + 0.146627566 + x = 2.649811247 + 0.146627566 Combine like terms: -0.146627566 + 0.146627566 = 0.000000000 0.000000000 + x = 2.649811247 + 0.146627566 x = 2.649811247 + 0.146627566 Combine like terms: 2.649811247 + 0.146627566 = 2.796438813 x = 2.796438813 Simplifying x = 2.796438813

Subproblem 2

x + -0.146627566 = -2.649811247 Simplifying x + -0.146627566 = -2.649811247 Reorder the terms: -0.146627566 + x = -2.649811247 Solving -0.146627566 + x = -2.649811247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.146627566' to each side of the equation. -0.146627566 + 0.146627566 + x = -2.649811247 + 0.146627566 Combine like terms: -0.146627566 + 0.146627566 = 0.000000000 0.000000000 + x = -2.649811247 + 0.146627566 x = -2.649811247 + 0.146627566 Combine like terms: -2.649811247 + 0.146627566 = -2.503183681 x = -2.503183681 Simplifying x = -2.503183681

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.796438813, -2.503183681}

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