-4.905x^2+29x-10=0

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Solution for -4.905x^2+29x-10=0 equation: 


Simplifying
-4.905x2 + 29x + -10 = 0

Reorder the terms:
-10 + 29x + -4.905x2 = 0

Solving
-10 + 29x + -4.905x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.905 the coefficient of the squared term: 

Divide each side by '-4.905'.
2.038735984 + -5.912334353x + x2 = 0

Move the constant term to the right:

Add '-2.038735984' to each side of the equation.
2.038735984 + -5.912334353x + -2.038735984 + x2 = 0 + -2.038735984

Reorder the terms:
2.038735984 + -2.038735984 + -5.912334353x + x2 = 0 + -2.038735984

Combine like terms: 2.038735984 + -2.038735984 = 0.000000000
0.000000000 + -5.912334353x + x2 = 0 + -2.038735984
-5.912334353x + x2 = 0 + -2.038735984

Combine like terms: 0 + -2.038735984 = -2.038735984
-5.912334353x + x2 = -2.038735984

The x term is -5.912334353x.  Take half its coefficient (-2.956167177).
Square it (8.738924378) and add it to both sides.

Add '8.738924378' to each side of the equation.
-5.912334353x + 8.738924378 + x2 = -2.038735984 + 8.738924378

Reorder the terms:
8.738924378 + -5.912334353x + x2 = -2.038735984 + 8.738924378

Combine like terms: -2.038735984 + 8.738924378 = 6.700188394
8.738924378 + -5.912334353x + x2 = 6.700188394

Factor a perfect square on the left side:
(x + -2.956167177)(x + -2.956167177) = 6.700188394

Calculate the square root of the right side: 2.588472212

Break this problem into two subproblems by setting 
(x + -2.956167177) equal to 2.588472212 and -2.588472212.


Subproblem 1
x + -2.956167177 = 2.588472212

Simplifying
x + -2.956167177 = 2.588472212

Reorder the terms:
-2.956167177 + x = 2.588472212

Solving
-2.956167177 + x = 2.588472212

Solving for variable 'x'.

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

Add '2.956167177' to each side of the equation.
-2.956167177 + 2.956167177 + x = 2.588472212 + 2.956167177

Combine like terms: -2.956167177 + 2.956167177 = 0.000000000
0.000000000 + x = 2.588472212 + 2.956167177
x = 2.588472212 + 2.956167177

Combine like terms: 2.588472212 + 2.956167177 = 5.544639389
x = 5.544639389

Simplifying
x = 5.544639389


Subproblem 2
x + -2.956167177 = -2.588472212

Simplifying
x + -2.956167177 = -2.588472212

Reorder the terms:
-2.956167177 + x = -2.588472212

Solving
-2.956167177 + x = -2.588472212

Solving for variable 'x'.

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

Add '2.956167177' to each side of the equation.
-2.956167177 + 2.956167177 + x = -2.588472212 + 2.956167177

Combine like terms: -2.956167177 + 2.956167177 = 0.000000000
0.000000000 + x = -2.588472212 + 2.956167177
x = -2.588472212 + 2.956167177

Combine like terms: -2.588472212 + 2.956167177 = 0.367694965
x = 0.367694965

Simplifying
x = 0.367694965


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.544639389, 0.367694965}

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