20x^2+19x-10=0

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Solution for 20x^2+19x-10=0 equation:


Simplifying
20x2 + 19x + -10 = 0

Reorder the terms:
-10 + 19x + 20x2 = 0

Solving
-10 + 19x + 20x2 = 0

Solving for variable 'x'.

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

Divide each side by '20'.
-0.5 + 0.95x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.95x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.95x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.95x + x2 = 0 + 0.5
0.95x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.95x + x2 = 0.5

The x term is 0.95x.  Take half its coefficient (0.475).
Square it (0.225625) and add it to both sides.

Add '0.225625' to each side of the equation.
0.95x + 0.225625 + x2 = 0.5 + 0.225625

Reorder the terms:
0.225625 + 0.95x + x2 = 0.5 + 0.225625

Combine like terms: 0.5 + 0.225625 = 0.725625
0.225625 + 0.95x + x2 = 0.725625

Factor a perfect square on the left side:
(x + 0.475)(x + 0.475) = 0.725625

Calculate the square root of the right side: 0.851836252

Break this problem into two subproblems by setting 
(x + 0.475) equal to 0.851836252 and -0.851836252.

Subproblem 1

x + 0.475 = 0.851836252 Simplifying x + 0.475 = 0.851836252 Reorder the terms: 0.475 + x = 0.851836252 Solving 0.475 + x = 0.851836252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.475' to each side of the equation. 0.475 + -0.475 + x = 0.851836252 + -0.475 Combine like terms: 0.475 + -0.475 = 0.000 0.000 + x = 0.851836252 + -0.475 x = 0.851836252 + -0.475 Combine like terms: 0.851836252 + -0.475 = 0.376836252 x = 0.376836252 Simplifying x = 0.376836252

Subproblem 2

x + 0.475 = -0.851836252 Simplifying x + 0.475 = -0.851836252 Reorder the terms: 0.475 + x = -0.851836252 Solving 0.475 + x = -0.851836252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.475' to each side of the equation. 0.475 + -0.475 + x = -0.851836252 + -0.475 Combine like terms: 0.475 + -0.475 = 0.000 0.000 + x = -0.851836252 + -0.475 x = -0.851836252 + -0.475 Combine like terms: -0.851836252 + -0.475 = -1.326836252 x = -1.326836252 Simplifying x = -1.326836252

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.376836252, -1.326836252}

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