-10x^2+21x-10=

Solution for -10x^2+21x-10= equation:

Simplifying
-10x2 + 21x + -10 = 0

Reorder the terms:
-10 + 21x + -10x2 = 0

Solving
-10 + 21x + -10x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
1 + -2.1x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.1x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -2.1x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.1x + x2 = 0 + -1
-2.1x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.1x + x2 = -1

The x term is -2.1x.  Take half its coefficient (-1.05).
Square it (1.1025) and add it to both sides.

Add '1.1025' to each side of the equation.
-2.1x + 1.1025 + x2 = -1 + 1.1025

Reorder the terms:
1.1025 + -2.1x + x2 = -1 + 1.1025

Combine like terms: -1 + 1.1025 = 0.1025
1.1025 + -2.1x + x2 = 0.1025

Factor a perfect square on the left side:
(x + -1.05)(x + -1.05) = 0.1025

Calculate the square root of the right side: 0.320156212

Break this problem into two subproblems by setting 
(x + -1.05) equal to 0.320156212 and -0.320156212.

Subproblem 1
x + -1.05 = 0.320156212

Simplifying
x + -1.05 = 0.320156212

Reorder the terms:
-1.05 + x = 0.320156212

Solving
-1.05 + x = 0.320156212

Solving for variable 'x'.

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

Add '1.05' to each side of the equation.
-1.05 + 1.05 + x = 0.320156212 + 1.05

Combine like terms: -1.05 + 1.05 = 0.00
0.00 + x = 0.320156212 + 1.05
x = 0.320156212 + 1.05

Combine like terms: 0.320156212 + 1.05 = 1.370156212
x = 1.370156212

Simplifying
x = 1.370156212

Subproblem 2
x + -1.05 = -0.320156212

Simplifying
x + -1.05 = -0.320156212

Reorder the terms:
-1.05 + x = -0.320156212

Solving
-1.05 + x = -0.320156212

Solving for variable 'x'.

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

Add '1.05' to each side of the equation.
-1.05 + 1.05 + x = -0.320156212 + 1.05

Combine like terms: -1.05 + 1.05 = 0.00
0.00 + x = -0.320156212 + 1.05
x = -0.320156212 + 1.05

Combine like terms: -0.320156212 + 1.05 = 0.729843788
x = 0.729843788

Simplifying
x = 0.729843788

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.370156212, 0.729843788}