7x^2-11x-29=0

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Solution for 7x^2-11x-29=0 equation:


Simplifying
7x2 + -11x + -29 = 0

Reorder the terms:
-29 + -11x + 7x2 = 0

Solving
-29 + -11x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-4.142857143 + -1.571428571x + x2 = 0

Move the constant term to the right:

Add '4.142857143' to each side of the equation.
-4.142857143 + -1.571428571x + 4.142857143 + x2 = 0 + 4.142857143

Reorder the terms:
-4.142857143 + 4.142857143 + -1.571428571x + x2 = 0 + 4.142857143

Combine like terms: -4.142857143 + 4.142857143 = 0.000000000
0.000000000 + -1.571428571x + x2 = 0 + 4.142857143
-1.571428571x + x2 = 0 + 4.142857143

Combine like terms: 0 + 4.142857143 = 4.142857143
-1.571428571x + x2 = 4.142857143

The x term is -1.571428571x.  Take half its coefficient (-0.7857142855).
Square it (0.6173469384) and add it to both sides.

Add '0.6173469384' to each side of the equation.
-1.571428571x + 0.6173469384 + x2 = 4.142857143 + 0.6173469384

Reorder the terms:
0.6173469384 + -1.571428571x + x2 = 4.142857143 + 0.6173469384

Combine like terms: 4.142857143 + 0.6173469384 = 4.7602040814
0.6173469384 + -1.571428571x + x2 = 4.7602040814

Factor a perfect square on the left side:
(x + -0.7857142855)(x + -0.7857142855) = 4.7602040814

Calculate the square root of the right side: 2.181789193

Break this problem into two subproblems by setting 
(x + -0.7857142855) equal to 2.181789193 and -2.181789193.

Subproblem 1

x + -0.7857142855 = 2.181789193 Simplifying x + -0.7857142855 = 2.181789193 Reorder the terms: -0.7857142855 + x = 2.181789193 Solving -0.7857142855 + x = 2.181789193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7857142855' to each side of the equation. -0.7857142855 + 0.7857142855 + x = 2.181789193 + 0.7857142855 Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000 0.0000000000 + x = 2.181789193 + 0.7857142855 x = 2.181789193 + 0.7857142855 Combine like terms: 2.181789193 + 0.7857142855 = 2.9675034785 x = 2.9675034785 Simplifying x = 2.9675034785

Subproblem 2

x + -0.7857142855 = -2.181789193 Simplifying x + -0.7857142855 = -2.181789193 Reorder the terms: -0.7857142855 + x = -2.181789193 Solving -0.7857142855 + x = -2.181789193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7857142855' to each side of the equation. -0.7857142855 + 0.7857142855 + x = -2.181789193 + 0.7857142855 Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000 0.0000000000 + x = -2.181789193 + 0.7857142855 x = -2.181789193 + 0.7857142855 Combine like terms: -2.181789193 + 0.7857142855 = -1.3960749075 x = -1.3960749075 Simplifying x = -1.3960749075

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.9675034785, -1.3960749075}

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