106x^2+743x-23478=0

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Solution for 106x^2+743x-23478=0 equation:


Simplifying
106x2 + 743x + -23478 = 0

Reorder the terms:
-23478 + 743x + 106x2 = 0

Solving
-23478 + 743x + 106x2 = 0

Solving for variable 'x'.

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

Divide each side by '106'.
-221.490566 + 7.009433962x + x2 = 0

Move the constant term to the right:

Add '221.490566' to each side of the equation.
-221.490566 + 7.009433962x + 221.490566 + x2 = 0 + 221.490566

Reorder the terms:
-221.490566 + 221.490566 + 7.009433962x + x2 = 0 + 221.490566

Combine like terms: -221.490566 + 221.490566 = 0.000000
0.000000 + 7.009433962x + x2 = 0 + 221.490566
7.009433962x + x2 = 0 + 221.490566

Combine like terms: 0 + 221.490566 = 221.490566
7.009433962x + x2 = 221.490566

The x term is 7.009433962x.  Take half its coefficient (3.504716981).
Square it (12.28304112) and add it to both sides.

Add '12.28304112' to each side of the equation.
7.009433962x + 12.28304112 + x2 = 221.490566 + 12.28304112

Reorder the terms:
12.28304112 + 7.009433962x + x2 = 221.490566 + 12.28304112

Combine like terms: 221.490566 + 12.28304112 = 233.77360712
12.28304112 + 7.009433962x + x2 = 233.77360712

Factor a perfect square on the left side:
(x + 3.504716981)(x + 3.504716981) = 233.77360712

Calculate the square root of the right side: 15.289656867

Break this problem into two subproblems by setting 
(x + 3.504716981) equal to 15.289656867 and -15.289656867.

Subproblem 1

x + 3.504716981 = 15.289656867 Simplifying x + 3.504716981 = 15.289656867 Reorder the terms: 3.504716981 + x = 15.289656867 Solving 3.504716981 + x = 15.289656867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.504716981' to each side of the equation. 3.504716981 + -3.504716981 + x = 15.289656867 + -3.504716981 Combine like terms: 3.504716981 + -3.504716981 = 0.000000000 0.000000000 + x = 15.289656867 + -3.504716981 x = 15.289656867 + -3.504716981 Combine like terms: 15.289656867 + -3.504716981 = 11.784939886 x = 11.784939886 Simplifying x = 11.784939886

Subproblem 2

x + 3.504716981 = -15.289656867 Simplifying x + 3.504716981 = -15.289656867 Reorder the terms: 3.504716981 + x = -15.289656867 Solving 3.504716981 + x = -15.289656867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.504716981' to each side of the equation. 3.504716981 + -3.504716981 + x = -15.289656867 + -3.504716981 Combine like terms: 3.504716981 + -3.504716981 = 0.000000000 0.000000000 + x = -15.289656867 + -3.504716981 x = -15.289656867 + -3.504716981 Combine like terms: -15.289656867 + -3.504716981 = -18.794373848 x = -18.794373848 Simplifying x = -18.794373848

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.784939886, -18.794373848}

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