25x^2-29x-57=0

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Solution for 25x^2-29x-57=0 equation:


Simplifying
25x2 + -29x + -57 = 0

Reorder the terms:
-57 + -29x + 25x2 = 0

Solving
-57 + -29x + 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'.
-2.28 + -1.16x + x2 = 0

Move the constant term to the right:

Add '2.28' to each side of the equation.
-2.28 + -1.16x + 2.28 + x2 = 0 + 2.28

Reorder the terms:
-2.28 + 2.28 + -1.16x + x2 = 0 + 2.28

Combine like terms: -2.28 + 2.28 = 0.00
0.00 + -1.16x + x2 = 0 + 2.28
-1.16x + x2 = 0 + 2.28

Combine like terms: 0 + 2.28 = 2.28
-1.16x + x2 = 2.28

The x term is -1.16x.  Take half its coefficient (-0.58).
Square it (0.3364) and add it to both sides.

Add '0.3364' to each side of the equation.
-1.16x + 0.3364 + x2 = 2.28 + 0.3364

Reorder the terms:
0.3364 + -1.16x + x2 = 2.28 + 0.3364

Combine like terms: 2.28 + 0.3364 = 2.6164
0.3364 + -1.16x + x2 = 2.6164

Factor a perfect square on the left side:
(x + -0.58)(x + -0.58) = 2.6164

Calculate the square root of the right side: 1.61752898

Break this problem into two subproblems by setting 
(x + -0.58) equal to 1.61752898 and -1.61752898.

Subproblem 1

x + -0.58 = 1.61752898 Simplifying x + -0.58 = 1.61752898 Reorder the terms: -0.58 + x = 1.61752898 Solving -0.58 + x = 1.61752898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.58' to each side of the equation. -0.58 + 0.58 + x = 1.61752898 + 0.58 Combine like terms: -0.58 + 0.58 = 0.00 0.00 + x = 1.61752898 + 0.58 x = 1.61752898 + 0.58 Combine like terms: 1.61752898 + 0.58 = 2.19752898 x = 2.19752898 Simplifying x = 2.19752898

Subproblem 2

x + -0.58 = -1.61752898 Simplifying x + -0.58 = -1.61752898 Reorder the terms: -0.58 + x = -1.61752898 Solving -0.58 + x = -1.61752898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.58' to each side of the equation. -0.58 + 0.58 + x = -1.61752898 + 0.58 Combine like terms: -0.58 + 0.58 = 0.00 0.00 + x = -1.61752898 + 0.58 x = -1.61752898 + 0.58 Combine like terms: -1.61752898 + 0.58 = -1.03752898 x = -1.03752898 Simplifying x = -1.03752898

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.19752898, -1.03752898}

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