4.905x^2+2x-.50=0

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Solution for 4.905x^2+2x-.50=0 equation:


Simplifying
4.905x2 + 2x + -0.50 = 0

Reorder the terms:
-0.50 + 2x + 4.905x2 = 0

Solving
-0.50 + 2x + 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'.
-0.1019367992 + 0.4077471967x + x2 = 0

Move the constant term to the right:

Add '0.1019367992' to each side of the equation.
-0.1019367992 + 0.4077471967x + 0.1019367992 + x2 = 0 + 0.1019367992

Reorder the terms:
-0.1019367992 + 0.1019367992 + 0.4077471967x + x2 = 0 + 0.1019367992

Combine like terms: -0.1019367992 + 0.1019367992 = 0.0000000000
0.0000000000 + 0.4077471967x + x2 = 0 + 0.1019367992
0.4077471967x + x2 = 0 + 0.1019367992

Combine like terms: 0 + 0.1019367992 = 0.1019367992
0.4077471967x + x2 = 0.1019367992

The x term is 0.4077471967x.  Take half its coefficient (0.2038735984).
Square it (0.04156444412) and add it to both sides.

Add '0.04156444412' to each side of the equation.
0.4077471967x + 0.04156444412 + x2 = 0.1019367992 + 0.04156444412

Reorder the terms:
0.04156444412 + 0.4077471967x + x2 = 0.1019367992 + 0.04156444412

Combine like terms: 0.1019367992 + 0.04156444412 = 0.14350124332
0.04156444412 + 0.4077471967x + x2 = 0.14350124332

Factor a perfect square on the left side:
(x + 0.2038735984)(x + 0.2038735984) = 0.14350124332

Calculate the square root of the right side: 0.37881558

Break this problem into two subproblems by setting 
(x + 0.2038735984) equal to 0.37881558 and -0.37881558.

Subproblem 1

x + 0.2038735984 = 0.37881558 Simplifying x + 0.2038735984 = 0.37881558 Reorder the terms: 0.2038735984 + x = 0.37881558 Solving 0.2038735984 + x = 0.37881558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2038735984' to each side of the equation. 0.2038735984 + -0.2038735984 + x = 0.37881558 + -0.2038735984 Combine like terms: 0.2038735984 + -0.2038735984 = 0.0000000000 0.0000000000 + x = 0.37881558 + -0.2038735984 x = 0.37881558 + -0.2038735984 Combine like terms: 0.37881558 + -0.2038735984 = 0.1749419816 x = 0.1749419816 Simplifying x = 0.1749419816

Subproblem 2

x + 0.2038735984 = -0.37881558 Simplifying x + 0.2038735984 = -0.37881558 Reorder the terms: 0.2038735984 + x = -0.37881558 Solving 0.2038735984 + x = -0.37881558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2038735984' to each side of the equation. 0.2038735984 + -0.2038735984 + x = -0.37881558 + -0.2038735984 Combine like terms: 0.2038735984 + -0.2038735984 = 0.0000000000 0.0000000000 + x = -0.37881558 + -0.2038735984 x = -0.37881558 + -0.2038735984 Combine like terms: -0.37881558 + -0.2038735984 = -0.5826891784 x = -0.5826891784 Simplifying x = -0.5826891784

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.1749419816, -0.5826891784}

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