47.5x^2-463.5x+927=0

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Solution for 47.5x^2-463.5x+927=0 equation:


Simplifying
47.5x2 + -463.5x + 927 = 0

Reorder the terms:
927 + -463.5x + 47.5x2 = 0

Solving
927 + -463.5x + 47.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '47.5'.
19.51578947 + -9.757894737x + x2 = 0

Move the constant term to the right:

Add '-19.51578947' to each side of the equation.
19.51578947 + -9.757894737x + -19.51578947 + x2 = 0 + -19.51578947

Reorder the terms:
19.51578947 + -19.51578947 + -9.757894737x + x2 = 0 + -19.51578947

Combine like terms: 19.51578947 + -19.51578947 = 0.00000000
0.00000000 + -9.757894737x + x2 = 0 + -19.51578947
-9.757894737x + x2 = 0 + -19.51578947

Combine like terms: 0 + -19.51578947 = -19.51578947
-9.757894737x + x2 = -19.51578947

The x term is -9.757894737x.  Take half its coefficient (-4.878947369).
Square it (23.80412743) and add it to both sides.

Add '23.80412743' to each side of the equation.
-9.757894737x + 23.80412743 + x2 = -19.51578947 + 23.80412743

Reorder the terms:
23.80412743 + -9.757894737x + x2 = -19.51578947 + 23.80412743

Combine like terms: -19.51578947 + 23.80412743 = 4.28833796
23.80412743 + -9.757894737x + x2 = 4.28833796

Factor a perfect square on the left side:
(x + -4.878947369)(x + -4.878947369) = 4.28833796

Calculate the square root of the right side: 2.070830259

Break this problem into two subproblems by setting 
(x + -4.878947369) equal to 2.070830259 and -2.070830259.


Subproblem 1
x + -4.878947369 = 2.070830259

Simplifying
x + -4.878947369 = 2.070830259

Reorder the terms:
-4.878947369 + x = 2.070830259

Solving
-4.878947369 + x = 2.070830259

Solving for variable 'x'.

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

Add '4.878947369' to each side of the equation.
-4.878947369 + 4.878947369 + x = 2.070830259 + 4.878947369

Combine like terms: -4.878947369 + 4.878947369 = 0.000000000
0.000000000 + x = 2.070830259 + 4.878947369
x = 2.070830259 + 4.878947369

Combine like terms: 2.070830259 + 4.878947369 = 6.949777628
x = 6.949777628

Simplifying
x = 6.949777628


Subproblem 2
x + -4.878947369 = -2.070830259

Simplifying
x + -4.878947369 = -2.070830259

Reorder the terms:
-4.878947369 + x = -2.070830259

Solving
-4.878947369 + x = -2.070830259

Solving for variable 'x'.

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

Add '4.878947369' to each side of the equation.
-4.878947369 + 4.878947369 + x = -2.070830259 + 4.878947369

Combine like terms: -4.878947369 + 4.878947369 = 0.000000000
0.000000000 + x = -2.070830259 + 4.878947369
x = -2.070830259 + 4.878947369

Combine like terms: -2.070830259 + 4.878947369 = 2.80811711
x = 2.80811711

Simplifying
x = 2.80811711


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.949777628, 2.80811711}

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