61.54=0.61x^2-.046x+1

Solution for 61.54=0.61x^2-.046x+1 equation:

Simplifying
61.54 = 0.61x2 + -0.046x + 1

Reorder the terms:
61.54 = 1 + -0.046x + 0.61x2

Solving
61.54 = 1 + -0.046x + 0.61x2

Solving for variable 'x'.

Combine like terms: 61.54 + -1 = 60.54
60.54 + 0.046x + -0.61x2 = 1 + -0.046x + 0.61x2 + -1 + 0.046x + -0.61x2

Reorder the terms:
60.54 + 0.046x + -0.61x2 = 1 + -1 + -0.046x + 0.046x + 0.61x2 + -0.61x2

Combine like terms: 1 + -1 = 0
60.54 + 0.046x + -0.61x2 = 0 + -0.046x + 0.046x + 0.61x2 + -0.61x2
60.54 + 0.046x + -0.61x2 = -0.046x + 0.046x + 0.61x2 + -0.61x2

Combine like terms: -0.046x + 0.046x = 0.000
60.54 + 0.046x + -0.61x2 = 0.000 + 0.61x2 + -0.61x2
60.54 + 0.046x + -0.61x2 = 0.61x2 + -0.61x2

Combine like terms: 0.61x2 + -0.61x2 = 0.00
60.54 + 0.046x + -0.61x2 = 0.00

Begin completing the square.  Divide all terms by
-0.61 the coefficient of the squared term: 

Divide each side by '-0.61'.
-99.24590164 + -0.07540983607x + x2 = 0

Move the constant term to the right:

Add '99.24590164' to each side of the equation.
-99.24590164 + -0.07540983607x + 99.24590164 + x2 = 0 + 99.24590164

Reorder the terms:
-99.24590164 + 99.24590164 + -0.07540983607x + x2 = 0 + 99.24590164

Combine like terms: -99.24590164 + 99.24590164 = 0.00000000
0.00000000 + -0.07540983607x + x2 = 0 + 99.24590164
-0.07540983607x + x2 = 0 + 99.24590164

Combine like terms: 0 + 99.24590164 = 99.24590164
-0.07540983607x + x2 = 99.24590164

The x term is -0.07540983607x.  Take half its coefficient (-0.03770491804).
Square it (0.001421660844) and add it to both sides.

Add '0.001421660844' to each side of the equation.
-0.07540983607x + 0.001421660844 + x2 = 99.24590164 + 0.001421660844

Reorder the terms:
0.001421660844 + -0.07540983607x + x2 = 99.24590164 + 0.001421660844

Combine like terms: 99.24590164 + 0.001421660844 = 99.247323300844
0.001421660844 + -0.07540983607x + x2 = 99.247323300844

Factor a perfect square on the left side:
(x + -0.03770491804)(x + -0.03770491804) = 99.247323300844

Calculate the square root of the right side: 9.962295082

Break this problem into two subproblems by setting 
(x + -0.03770491804) equal to 9.962295082 and -9.962295082.

Subproblem 1
x + -0.03770491804 = 9.962295082

Simplifying
x + -0.03770491804 = 9.962295082

Reorder the terms:
-0.03770491804 + x = 9.962295082

Solving
-0.03770491804 + x = 9.962295082

Solving for variable 'x'.

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

Add '0.03770491804' to each side of the equation.
-0.03770491804 + 0.03770491804 + x = 9.962295082 + 0.03770491804

Combine like terms: -0.03770491804 + 0.03770491804 = 0.00000000000
0.00000000000 + x = 9.962295082 + 0.03770491804
x = 9.962295082 + 0.03770491804

Combine like terms: 9.962295082 + 0.03770491804 = 10.00000000004
x = 10.00000000004

Simplifying
x = 10.00000000004

Subproblem 2
x + -0.03770491804 = -9.962295082

Simplifying
x + -0.03770491804 = -9.962295082

Reorder the terms:
-0.03770491804 + x = -9.962295082

Solving
-0.03770491804 + x = -9.962295082

Solving for variable 'x'.

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

Add '0.03770491804' to each side of the equation.
-0.03770491804 + 0.03770491804 + x = -9.962295082 + 0.03770491804

Combine like terms: -0.03770491804 + 0.03770491804 = 0.00000000000
0.00000000000 + x = -9.962295082 + 0.03770491804
x = -9.962295082 + 0.03770491804

Combine like terms: -9.962295082 + 0.03770491804 = -9.92459016396
x = -9.92459016396

Simplifying
x = -9.92459016396

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.00000000004, -9.92459016396}