-7x^2+33x-10=0

Solution for -7x^2+33x-10=0 equation:

Simplifying
-7x2 + 33x + -10 = 0

Reorder the terms:
-10 + 33x + -7x2 = 0

Solving
-10 + 33x + -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'.
1.428571429 + -4.714285714x + x2 = 0

Move the constant term to the right:

Add '-1.428571429' to each side of the equation.
1.428571429 + -4.714285714x + -1.428571429 + x2 = 0 + -1.428571429

Reorder the terms:
1.428571429 + -1.428571429 + -4.714285714x + x2 = 0 + -1.428571429

Combine like terms: 1.428571429 + -1.428571429 = 0.000000000
0.000000000 + -4.714285714x + x2 = 0 + -1.428571429
-4.714285714x + x2 = 0 + -1.428571429

Combine like terms: 0 + -1.428571429 = -1.428571429
-4.714285714x + x2 = -1.428571429

The x term is -4.714285714x.  Take half its coefficient (-2.357142857).
Square it (5.556122448) and add it to both sides.

Add '5.556122448' to each side of the equation.
-4.714285714x + 5.556122448 + x2 = -1.428571429 + 5.556122448

Reorder the terms:
5.556122448 + -4.714285714x + x2 = -1.428571429 + 5.556122448

Combine like terms: -1.428571429 + 5.556122448 = 4.127551019
5.556122448 + -4.714285714x + x2 = 4.127551019

Factor a perfect square on the left side:
(x + -2.357142857)(x + -2.357142857) = 4.127551019

Calculate the square root of the right side: 2.031637522

Break this problem into two subproblems by setting 
(x + -2.357142857) equal to 2.031637522 and -2.031637522.

Subproblem 1
x + -2.357142857 = 2.031637522

Simplifying
x + -2.357142857 = 2.031637522

Reorder the terms:
-2.357142857 + x = 2.031637522

Solving
-2.357142857 + x = 2.031637522

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.357142857' to each side of the equation.
-2.357142857 + 2.357142857 + x = 2.031637522 + 2.357142857

Combine like terms: -2.357142857 + 2.357142857 = 0.000000000
0.000000000 + x = 2.031637522 + 2.357142857
x = 2.031637522 + 2.357142857

Combine like terms: 2.031637522 + 2.357142857 = 4.388780379
x = 4.388780379

Simplifying
x = 4.388780379

Subproblem 2
x + -2.357142857 = -2.031637522

Simplifying
x + -2.357142857 = -2.031637522

Reorder the terms:
-2.357142857 + x = -2.031637522

Solving
-2.357142857 + x = -2.031637522

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.357142857' to each side of the equation.
-2.357142857 + 2.357142857 + x = -2.031637522 + 2.357142857

Combine like terms: -2.357142857 + 2.357142857 = 0.000000000
0.000000000 + x = -2.031637522 + 2.357142857
x = -2.031637522 + 2.357142857

Combine like terms: -2.031637522 + 2.357142857 = 0.325505335
x = 0.325505335

Simplifying
x = 0.325505335

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.388780379, 0.325505335}