2.5x^2=4.75x-2.1

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Solution for 2.5x^2=4.75x-2.1 equation: 


Simplifying
2.5x2 = 4.75x + -2.1

Reorder the terms:
2.5x2 = -2.1 + 4.75x

Solving
2.5x2 = -2.1 + 4.75x

Solving for variable 'x'.

Reorder the terms:
2.1 + -4.75x + 2.5x2 = -2.1 + 4.75x + 2.1 + -4.75x

Reorder the terms:
2.1 + -4.75x + 2.5x2 = -2.1 + 2.1 + 4.75x + -4.75x

Combine like terms: -2.1 + 2.1 = 0.0
2.1 + -4.75x + 2.5x2 = 0.0 + 4.75x + -4.75x
2.1 + -4.75x + 2.5x2 = 4.75x + -4.75x

Combine like terms: 4.75x + -4.75x = 0.00
2.1 + -4.75x + 2.5x2 = 0.00

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

Divide each side by '2.5'.
0.84 + -1.9x + x2 = 0.0

Move the constant term to the right:

Add '-0.84' to each side of the equation.
0.84 + -1.9x + -0.84 + x2 = 0.0 + -0.84

Reorder the terms:
0.84 + -0.84 + -1.9x + x2 = 0.0 + -0.84

Combine like terms: 0.84 + -0.84 = 0.00
0.00 + -1.9x + x2 = 0.0 + -0.84
-1.9x + x2 = 0.0 + -0.84

Combine like terms: 0.0 + -0.84 = -0.84
-1.9x + x2 = -0.84

The x term is -1.9x.  Take half its coefficient (-0.95).
Square it (0.9025) and add it to both sides.

Add '0.9025' to each side of the equation.
-1.9x + 0.9025 + x2 = -0.84 + 0.9025

Reorder the terms:
0.9025 + -1.9x + x2 = -0.84 + 0.9025

Combine like terms: -0.84 + 0.9025 = 0.0625
0.9025 + -1.9x + x2 = 0.0625

Factor a perfect square on the left side:
(x + -0.95)(x + -0.95) = 0.0625

Calculate the square root of the right side: 0.25

Break this problem into two subproblems by setting 
(x + -0.95) equal to 0.25 and -0.25.


Subproblem 1
x + -0.95 = 0.25

Simplifying
x + -0.95 = 0.25

Reorder the terms:
-0.95 + x = 0.25

Solving
-0.95 + x = 0.25

Solving for variable 'x'.

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

Add '0.95' to each side of the equation.
-0.95 + 0.95 + x = 0.25 + 0.95

Combine like terms: -0.95 + 0.95 = 0.00
0.00 + x = 0.25 + 0.95
x = 0.25 + 0.95

Combine like terms: 0.25 + 0.95 = 1.2
x = 1.2

Simplifying
x = 1.2


Subproblem 2
x + -0.95 = -0.25

Simplifying
x + -0.95 = -0.25

Reorder the terms:
-0.95 + x = -0.25

Solving
-0.95 + x = -0.25

Solving for variable 'x'.

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

Add '0.95' to each side of the equation.
-0.95 + 0.95 + x = -0.25 + 0.95

Combine like terms: -0.95 + 0.95 = 0.00
0.00 + x = -0.25 + 0.95
x = -0.25 + 0.95

Combine like terms: -0.25 + 0.95 = 0.7
x = 0.7

Simplifying
x = 0.7


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2, 0.7}

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