25x^2+63x-20=0

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Solution for 25x^2+63x-20=0 equation:


Simplifying
25x2 + 63x + -20 = 0

Reorder the terms:
-20 + 63x + 25x2 = 0

Solving
-20 + 63x + 25x2 = 0

Solving for variable 'x'.

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

Divide each side by '25'.
-0.8 + 2.52x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 2.52x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 2.52x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 2.52x + x2 = 0 + 0.8
2.52x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
2.52x + x2 = 0.8

The x term is 2.52x.  Take half its coefficient (1.26).
Square it (1.5876) and add it to both sides.

Add '1.5876' to each side of the equation.
2.52x + 1.5876 + x2 = 0.8 + 1.5876

Reorder the terms:
1.5876 + 2.52x + x2 = 0.8 + 1.5876

Combine like terms: 0.8 + 1.5876 = 2.3876
1.5876 + 2.52x + x2 = 2.3876

Factor a perfect square on the left side:
(x + 1.26)(x + 1.26) = 2.3876

Calculate the square root of the right side: 1.545186073

Break this problem into two subproblems by setting 
(x + 1.26) equal to 1.545186073 and -1.545186073.

Subproblem 1

x + 1.26 = 1.545186073 Simplifying x + 1.26 = 1.545186073 Reorder the terms: 1.26 + x = 1.545186073 Solving 1.26 + x = 1.545186073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.26' to each side of the equation. 1.26 + -1.26 + x = 1.545186073 + -1.26 Combine like terms: 1.26 + -1.26 = 0.00 0.00 + x = 1.545186073 + -1.26 x = 1.545186073 + -1.26 Combine like terms: 1.545186073 + -1.26 = 0.285186073 x = 0.285186073 Simplifying x = 0.285186073

Subproblem 2

x + 1.26 = -1.545186073 Simplifying x + 1.26 = -1.545186073 Reorder the terms: 1.26 + x = -1.545186073 Solving 1.26 + x = -1.545186073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.26' to each side of the equation. 1.26 + -1.26 + x = -1.545186073 + -1.26 Combine like terms: 1.26 + -1.26 = 0.00 0.00 + x = -1.545186073 + -1.26 x = -1.545186073 + -1.26 Combine like terms: -1.545186073 + -1.26 = -2.805186073 x = -2.805186073 Simplifying x = -2.805186073

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.285186073, -2.805186073}

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