35x^2-43x-12=

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Solution for 35x^2-43x-12= equation:


Simplifying
35x2 + -43x + -12 = 0

Reorder the terms:
-12 + -43x + 35x2 = 0

Solving
-12 + -43x + 35x2 = 0

Solving for variable 'x'.

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

Divide each side by '35'.
-0.3428571429 + -1.228571429x + x2 = 0

Move the constant term to the right:

Add '0.3428571429' to each side of the equation.
-0.3428571429 + -1.228571429x + 0.3428571429 + x2 = 0 + 0.3428571429

Reorder the terms:
-0.3428571429 + 0.3428571429 + -1.228571429x + x2 = 0 + 0.3428571429

Combine like terms: -0.3428571429 + 0.3428571429 = 0.0000000000
0.0000000000 + -1.228571429x + x2 = 0 + 0.3428571429
-1.228571429x + x2 = 0 + 0.3428571429

Combine like terms: 0 + 0.3428571429 = 0.3428571429
-1.228571429x + x2 = 0.3428571429

The x term is -1.228571429x.  Take half its coefficient (-0.6142857145).
Square it (0.3773469390) and add it to both sides.

Add '0.3773469390' to each side of the equation.
-1.228571429x + 0.3773469390 + x2 = 0.3428571429 + 0.3773469390

Reorder the terms:
0.3773469390 + -1.228571429x + x2 = 0.3428571429 + 0.3773469390

Combine like terms: 0.3428571429 + 0.3773469390 = 0.7202040819
0.3773469390 + -1.228571429x + x2 = 0.7202040819

Factor a perfect square on the left side:
(x + -0.6142857145)(x + -0.6142857145) = 0.7202040819

Calculate the square root of the right side: 0.848648385

Break this problem into two subproblems by setting 
(x + -0.6142857145) equal to 0.848648385 and -0.848648385.

Subproblem 1

x + -0.6142857145 = 0.848648385 Simplifying x + -0.6142857145 = 0.848648385 Reorder the terms: -0.6142857145 + x = 0.848648385 Solving -0.6142857145 + x = 0.848648385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6142857145' to each side of the equation. -0.6142857145 + 0.6142857145 + x = 0.848648385 + 0.6142857145 Combine like terms: -0.6142857145 + 0.6142857145 = 0.0000000000 0.0000000000 + x = 0.848648385 + 0.6142857145 x = 0.848648385 + 0.6142857145 Combine like terms: 0.848648385 + 0.6142857145 = 1.4629340995 x = 1.4629340995 Simplifying x = 1.4629340995

Subproblem 2

x + -0.6142857145 = -0.848648385 Simplifying x + -0.6142857145 = -0.848648385 Reorder the terms: -0.6142857145 + x = -0.848648385 Solving -0.6142857145 + x = -0.848648385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6142857145' to each side of the equation. -0.6142857145 + 0.6142857145 + x = -0.848648385 + 0.6142857145 Combine like terms: -0.6142857145 + 0.6142857145 = 0.0000000000 0.0000000000 + x = -0.848648385 + 0.6142857145 x = -0.848648385 + 0.6142857145 Combine like terms: -0.848648385 + 0.6142857145 = -0.2343626705 x = -0.2343626705 Simplifying x = -0.2343626705

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.4629340995, -0.2343626705}

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