20x^2+79x-45=0

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Solution for 20x^2+79x-45=0 equation:


Simplifying
20x2 + 79x + -45 = 0

Reorder the terms:
-45 + 79x + 20x2 = 0

Solving
-45 + 79x + 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'.
-2.25 + 3.95x + x2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 3.95x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 3.95x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 3.95x + x2 = 0 + 2.25
3.95x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
3.95x + x2 = 2.25

The x term is 3.95x.  Take half its coefficient (1.975).
Square it (3.900625) and add it to both sides.

Add '3.900625' to each side of the equation.
3.95x + 3.900625 + x2 = 2.25 + 3.900625

Reorder the terms:
3.900625 + 3.95x + x2 = 2.25 + 3.900625

Combine like terms: 2.25 + 3.900625 = 6.150625
3.900625 + 3.95x + x2 = 6.150625

Factor a perfect square on the left side:
(x + 1.975)(x + 1.975) = 6.150625

Calculate the square root of the right side: 2.480045362

Break this problem into two subproblems by setting 
(x + 1.975) equal to 2.480045362 and -2.480045362.

Subproblem 1

x + 1.975 = 2.480045362 Simplifying x + 1.975 = 2.480045362 Reorder the terms: 1.975 + x = 2.480045362 Solving 1.975 + x = 2.480045362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.975' to each side of the equation. 1.975 + -1.975 + x = 2.480045362 + -1.975 Combine like terms: 1.975 + -1.975 = 0.000 0.000 + x = 2.480045362 + -1.975 x = 2.480045362 + -1.975 Combine like terms: 2.480045362 + -1.975 = 0.505045362 x = 0.505045362 Simplifying x = 0.505045362

Subproblem 2

x + 1.975 = -2.480045362 Simplifying x + 1.975 = -2.480045362 Reorder the terms: 1.975 + x = -2.480045362 Solving 1.975 + x = -2.480045362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.975' to each side of the equation. 1.975 + -1.975 + x = -2.480045362 + -1.975 Combine like terms: 1.975 + -1.975 = 0.000 0.000 + x = -2.480045362 + -1.975 x = -2.480045362 + -1.975 Combine like terms: -2.480045362 + -1.975 = -4.455045362 x = -4.455045362 Simplifying x = -4.455045362

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.505045362, -4.455045362}

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